Suppose we are given an arbitrary form for the acceleration a(t) of a particle that starts from rest at r(t_i)=0. What would be the derivation of its' position at r(t_f): a)(t_f  t_i)⌠t_f a(t)dt ⌡t_i b) v(t_f)+v(t_i)/2 ((t_ft_i)) c)⌠t_f dt
46,547 results
Cal
If the equation of motion of a particle is given by s = A cos(ωt + δ), the particle is said to undergo simple harmonic motion. s'(t) = Aω sin(ωt + δ) When is the velocity 0? (Use n as the arbitrary integer.) t= _____________ I thought it was 0, but

physics
At t= 0, a particle starts from rest at x= 0, y= 0, and moves in the xy plane with an acceleration >a (vector) = (4.0ihat+ 3.0jhat)m/s^2. Assume t is in seconds. Determine the x component of velocity as a function of time t. Determine the y component of

physics
The velocityversustime graph is shown for a particle moving along the xaxis. Its initial position is x0 = 1.8m at t0 =0s. Part A What is the particle's position at t=1.0s? Part B What is the particle's acceleration at t= 1.0s? Part C What is the

Physics
To find the velocity and acceleration vectors for uniform circular motion and to recognize that this acceleration is the centripetal acceleration. Suppose that a particle's position is given by the following expression: r(t) = Rcos(omega*t)i +

physics
A particle starts moving with acceleration 2 m/s2. distance travelled by it in 5th half second is..??

calculus
5. A particle moves along the xaxis in such a way that its position at time t is given by x=3t^416t^3+24t^2 for 5 ≤ t ≤ 5. a. Determine the velocity and acceleration of the particle at time t. b. At what values of t is the particle at rest? c. At

Physics
A 0.500 kg particle moves in a circle of R=0.0150 m at constant speed. The time for 20 complete revolutions is 31.7 s. What is the period T of the motion? What is the speed of the particle? What is the centripetal acceleration of the particle? What is the

physics
The position of a particle moving along an x axis is given by x = 15t2  2.0t3, where x is in meters and t is in seconds. (a) Determine the position, velocity, and acceleration of the particle at t = 3.0 s. x = m v = m/s a = m/s2 (b) What is the maximum

math
a particle starts at time t = 0 and moves along the x  axis so that its position at any time t is greater than or equal to zero is given x(t) = (t1)^3(2t3) A. Find the velocity of the particle at any time t greater than or equal to 0. B. For what values

physics
A particle moving with a constant acceleration describes in the last second of it's motion 9/25th of the whole distance.of it starts from rest ,how long is the particle is in motion and through what distance does it move if it describes 6cm in first

Dynamics
A particle moves in accordance with the equation s=32+24t2t? Find a) vt relationship b) How far to the right of the origin does the particle go? c) s when t=0 d) acceleration of the particle at t=3sec

Physics
A particle starts from the origin at t = 0 and moves along the positive x axis. A graph of the velocity of the particle as a function of the time is shown in the figure; the vaxis scale is set by vs = 7.0 m/s. (a) What is the coordinate of the particle at

physic
A 1.57kg particle initially at rest and at the origin of an xy coordinate system is subjected to a timedependent force of F(t) = (7.00ti − 8.00j)N with t in seconds. (a) At what time t will the particle's speed be 19.0 m/s? s (b) How far from the

science
the velocity of a particle is given by v=[16t^2i+4t^3j +(5t+2)k]m/s, where t is in seconds. If the particle is at the origin when t=0, determine the magnitude of the particle's acceleration when t=2s. What is the x,y,z coordinate position of the particle

physics
The equation of motion of a particle in vertical SHM is given by y = (10 cm) sin 0.80t. (a) What is the particle's displacement at t = 1.1 s? (b) What is the particle's velocity at t = 1.1 s? (c) What is the particle's acceleration at t = 1.1 s?

Physics
A particle starts from the origin at t = 0 with an initial velocity of 4.8m/s along the positive x axis.If the acceleration is (2.5 i^ + 4.3 j^)m/s2, determine (a)the velocity and (b)position of the particle at the moment it reaches its maximum x

Calculus
A particle starts at the point (5,0) at t=0 and moves along the xaxis in such a way that at time t>0 its velocity v(t) is given by v(t)= t/(1+t^2). a). Determine the maximum velocity of the particle. Justify your answer. b). Determine the position of the

physics
Two particles A and B are in uniform circular motion about a common center. The acceleration of particle A is 4.7 times that of particle B. Particle B takes 2.4 times as long for a rotation as particle A. Th ratio of the radius of the motion of particle A

Calculus
Let f be the function given by f(t) = 2ðt + sin(2ðt) a) Find the value of t in the open interval (0,20 for which the line tangent at (t, f(t)) is parallel to the line through (0,0) and (2,4ð) b) Suppose the given function describes the position of a

Calculus
a particle starts at time t = 0 and moves along the x axis so that its position at any time t>= 0 is given by x(t) = ((t1)^3)(2t3) a.find the velocity of the particle at any time t>= 0 b. for what values of t is the velocity of the particle negative? c.

Calculus
A particle moves along the graph of the function y= 8/3x^(3/2) at the constant rate of 3 units per minute. The particle starts at the point where x = 1 and travels in the direction of increasing x. After one hour, what is the xvalue, rounded to the

physics
A particle starts from the origin at t = 0 with an initial velocity of 5.5 m/s along the positive x axis.If the acceleration is (2.8i + 4.1jm/s^2, determine (a)the velocity and (b)position of the particle at the moment it reaches its maximum x coordinate.

Physics
At t=0 a particle starts from rest at x=0, y=0 and moves in the xy plane with an acceleration a=(4.0i+3.0j)m/s^2. Determine (a) the x and y components of velocity, (b) the speed of the particle, and (c) the position of the particle, all as a function of

physics
A body starts with an initial velocity of 10m/s and moves along a straight line with a constant acceleration. When the velocity of the particle becomes 50 m/s the acceleration is reversed in direction without changing magnitude. Find the velocity of the

physics
A particle starts from the origin with a velocity of 6.0 i m/s and moves in the xy plane with a constant acceleration of (2.0i + 4.0j)m/s^2 . at he instant the particle achieves maximum positive xcoordinate, how far is it from the origin?

phys
At t= 0, a particle starts from rest at x= 0, y= 0, and moves in the xy plane with an acceleration >a = (4.0ihat+ 3.0jhat)m/s^2. Assume t is in seconds. Determine the position of the particle as a function of time t. Express your answer in terms of the

HS Calculus
Having trouble with this questions. Please help. A particle moves on the xaxis so that its position at any time t (is greater than or equal to) 0 is given by x(t) = 2te^t a) Find the acceleration of the particle at t=0 b)find the velocity of the particle

physics
a particle starts moving from rest with uniform acceleration . it travels a distance y in the next 2 sec

Physics
A particle starts at the origin at t=0 with an intial velocity of 5.0m/s along the positive x axis. If the acceleration is (3.0,4.5) m/s^2, determine the velocity and position of the particle at the moment it reaches its maximum x coordinate. You can't

Calculus
If the equation of motion of a particle is given by s = A cos(ωt + δ), the particle is said to undergo simple harmonic motion. (a) Find the velocity of the particle at time t. s'(t) =  A ω sin(ωt + δ) I figured out how to do part a, but I don't know

Calculus
The position of a particle moving on a horizontal line is given by s(t)=2t^315t^2+24t5, where s is measured in feet and t in seconds. a: What is the initial position of the particle? b: What is the average velocity of the particle on the interval

calculus
5. A particle moves along the y – axis with velocity given by v(t)=tsine(t^2) for t>=0 . a. In which direction (up or down) is the particle moving at time t = 1.5? Why? b. Find the acceleration of the particle at time t= 1.5. Is the velocity of the

calculus
4. A particle starts at the point (5, 0) at t = 0 and moves along the xaxis in such a way that at time t > 0 the velocity is given by v(t)=t/(1+t^2) a. Determine the maximum velocity attained by the particle. Justify your answer. b. Determine the position

Physics
A particle starts from rest and moves with a constant acceleration of 0.5m/s2. Calculate the time taken by the particle to cover a distance of 25m.

physics
Suppose we are given an arbitrary form for the acceleration a(t) of a particle that starts from rest at r(t_i)=0. What would be the derivation of its' position at r(t_f): a)(t_f  t_i)⌠t_f a(t)dt ⌡t_i b) v(t_f)+v(t_i)/2 ((t_ft_i)) c)⌠t_f dt ⌠t

physics help
The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time interval from t = 1

physics
A particle starts from the origin at t = 0 with an initial velocity of 5.4m/s along the positive x axis.If the acceleration is (3.4 i + 4.9 j )m/s^2, determine (a)the velocity and (b)position of the particle at the moment it reaches its maximum x

physics
Two particles, with identical positive charges and a separation of 2.60 x 10^2 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1 whose magnitude is 4.60 x 10^3 m/s^2, while particle 2 has an acceleration a 2 whose

calculus
let f(t) = 2*pi*t + sin(2*pi*t) a) find value of t in open interval (0,2) for which the tangent line at (t, f(t)) is parallel to the line through (0,0( and (2, 4pi) b) suppose the given funtion describes the position of a particle on the xaxis for 0

Physicscan anyone check my work?
A particle starts from the origin with velocity 2i m/s at t = 0 and moves in the xy plane with a varying acceleration given by 2 (sq root t) where is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function

Calculus
I don't understand what the graph is suppose to show and what the integral equation is suppose to mean. How would I use the graph to answer the questions? f is the differentiable function whose graph is shown in the figure. The position at time t (sec) of

math
Consider a particle moving along the xaxis where x(t) is the position of the particle at time t, x' (t) is its velocity, and x'' (t) is its acceleration. x(t) = t3 − 12t2 + 21t − 7, 0 ≤ t ≤ 10 (a) Find the velocity and acceleration of the

College Physics
Two equally charged particles, held 2.8 x 103 m apart, are released from rest. The initial acceleration of the first particle is observed to be 6.8 m/s2 and that of the second to be 6.8 m/s2. If the mass of the first particle is 5.3 x 107 kg, what are

physics
a particle at rest starts in horizontal strsight line with uniform acceleration ratio distance during 4th and 3rd sec ond

Math
The onedimensional displacement, s meters of a particle, after t seconds, is given by the function s=t(t4)^2. (i) when does the particle have zero acceleration? (ii) where is the particle at this time and what is it doing?

calculus
a particle starts from rest and moves along a straight line with an acceleration equal to 2415√t where distance and time are measured in terms of feet and seconds respectively. with what acceleration will the particle return to the starting point? help

calculus
a particle starts from rest and moves along a straight line with an acceleration equal to 2415√t where distance and time are measured in terms of feet and seconds respectively. with what acceleration will the particle return to the starting point?

calculus
a particle starts from rest and moves along a straight line with an acceleration equal to 2415√t where distance and time are measured in terms of feet and seconds respectively. with what acceleration will the particle return to the starting point?

dynamics
The acceleration of a particle is defined by the relation a = 60x^1.5, where a is expressed in m/s^2 and x in meters. Knowing that the particle starts with no initial velocity at x = 4 m, determine the velocity of the particle when x = 2 m, x = 1 m, x =

Physics
A particle starts from rest and has an acceleration of 2m/s*2 for 10sec.After that, the particle travels for 30sec with constant speed and then undergoes a retardation of 4m/s*2 and comes back to rest. The total distance covered by the particle is?

physics help
The magnitude of the velocity of a particle which starts from rest 2 ft below the origin when t = 0 and moves along a vertical axis is directly proportional to the time after starting. The displacement of the particle during the time interval from t = 1

science
A particle starts from the origin with a velocity of 10 m/s and moves with a constant acceleration till the velocity increases to 50 m/s. At that instant the acceleration is suddenly reversed. What will be the velocity of the particle, when it returns to

physic
Three forces F1 = (80.90i − 54.63j) N, F2 = (23.50i − 80.52j) N, and F3 = (−104.4i + 361.9j) N are exerted on a particle. The particle's mass is 23.11 kg. Find the particle's acceleration. (Express your answer in vector form.) a = m/s2

math
A particle is traveling along a onedimensional path (such as a number line). The position of the particle is governed by the time function x(t) ƒ 3t 4 ƒ{16t3 ƒy18t 2 ƒy 2 , where t is in minutes and 0 „T t „T 5 . Answer the following questions.

Phyics
A particle, which starts from rest, covers a distance of 19.94 cm in the first 8.6 seconds. Find the acceleration (in m/s2) of the particle at the end of 8.6 seconds.

Physics
A particle starts from the origin at t = 0 with an initial velocity of 8.0 m/s along the positive x axis. If the acceleration is (3.7 + 2.5 ) m/s2, determine the velocity and position of the particle at the moment it reaches its maximum x coordinate.

physics
A particle starts frm a point with a velocity of 6m/s and moves with an acceleration of (2m/secondsquare). Show that after 6 seconds the particle will beat the starting point ? Plz explain....

Maths
a particle starts from rest at o and moves in a straight line so that t seconds after, its velocity vm/s is given by v=2tt^2. given that particle comes instantanuously at rest at p. Find i) time taken to reach p? ii) the acceleration at p? iii) distance

calculus
At t=0 , a particle starts at the origin with a velocity of 6 feet per second and moves along the xaxis in such a way that at time t its acceleration is 12t^2 feet per second per second. Through how many feet does the particle move during the first 2

physics
trying to study but stuck on this problem. Two particles, with identical positive charges and a separation of 2.34 x 102 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1 whose magnitude is 6.75 x 103 m/s2, while

Physics (Algerbrabased)
A particle is moving clockwise around a circle with a radius 3.31 m. The magnitude of the total acceleration of the particle at the given instant is 14.3 m/s^2; the angle between the vector of total acceleration and the radiusvector of the particle is

math
Which three options are true about motion in a straight line. A. A particle which moves at an increasing velocity has a constant acceleration. B. If two particles always have the same velocity as each other, their separation does not change. C. A particle

calculous
A particle moves on the x –axis so that its position at any time is given by x(t) = 2t3 + 1. a. Find the acceleration of the particle at t = 0. b. Find the velocity of the particle when its acceleration is 0. c. Find the total distance traveled by the

AP Calculous
A particle moves on the x –axis so that its position at any time is given by x(t) = 2t3 + 1. a. Find the acceleration of the particle at t = 0. b. Find the velocity of the particle when its acceleration is 0. c. Find the total distance traveled by the

Physics
I've managed to figure out question B but cannot figure out A, any help appreciated Two particles, with identical positive charges and separation of 3.04 × 102 m, are released from rest. Immediately after the release, particle 1 has an acceleration a1

Maths mst
Question – 3: Consider a particle moving according to the velocity function, v(t) = 2a3exp(2t)+2/t+2,for t>0. (a) If the net distance,d,covered by the particle in the time interval,[0,3],is 20,find the value of a. What is the terminal velocity of the

Dynamics
The acceleration of a particle moving along a straight line is inversely proportional to its speed with the constant of porpotionality being k. The body starts from the position s = x0 ^i with initial speed v0. Determine the velocity of the particle as a

Physics
A body moved on xaxis at time t secs, the displacement of the particle from the origin is xmetre and the velocity of the particle is vm/s when t=0, s=0 and v=0. 1) given that the particle moves at a constant acceleration and that v=1 when t=4, find a)the

Physics
Two particles, with identical positive charges and a separation of 2.65 102 m, are released from rest. Immediately after the release, particle 1 has an acceleration 1 whose magnitude is 4.25 103 m/s2, while particle 2 has an acceleration 2 whose magnitude

math
A particle moves along straight line such that its displacement S meters from a given point is S = t^3 – 5t^2 + 4 whee t is time in seconds. Find (a) The displacement of particle at t = 5 (b) The velocity of the particle when t = 5 (c) The values of t

physics
A particle is traveling counterclockwise in a circle of radius r = 2.85 m. At some instant in time, the particle is located by the angular coordinate Î± = 34.0Â°, the total acceleration has a magnitude of a = 19.0 m/s2 and is directed at an angle Î²

Physics #16
Two particles, with identical positive charges and a separation of 2.65 102 m, are released from rest. Immediately after the release, particle 1 has an acceleration 1 whose magnitude is 4.25 103 m/s2, while particle 2 has an acceleration 2 whose magnitude

physics help!
The equation of motion of a particle in vertical SHM is given by y = (17 cm) sin 0.70t. (a) What is the particle's displacement at t = 1.1 s? (b) What is the particle's velocity at t = 1.1 s?(c) What is the particle's acceleration at t = 1.1 s?

Calculus (Answer Check)
Are my answers right? If they are wrong you don't have to tell me how to do it its okay =) A particle starts at time t=0 and moves along the xaxis so that its position at any time t(greater or equal to) 0 is given by x(t)=(t1)^3 (2t3) 1.find the

Math
A particle is projected along an inclined plane with a velocity given by the formula v = 4.4t2 + 10.1t 23.2. Determine the acceleration of the particle when t = 1.5 s. acceleration in m/s2 = My Answer V'=8.8t+10.1 V"=8.8 V"(1.5)= 8.8 acceleration in m/s2

Physics
A particle starts from the origin with velocity 2i m/s at t = 0 and moves in the xy plane with a varying acceleration given by 2 (sq root t) where is in meters per second squared and t is in seconds. (a) Determine the velocity of the particle as a function

maths
Which three options are true about motion in a straight line. A. A particle which moves at an increasing velocity has a constant acceleration. B. If two particles always have the same velocity as each other, their separation does not change. C. A particle

Physics
A particle starts from rest and travels in a circular path of diameter 10.0 m. If the tangential component of its acceleration is 2.5 m/s2, determine (a) the speed at the instant it has traveled one third of a lap around the circle, and (b) the magnitude

Math
A particle moves in a linear motion according to: s = 10  6t2. Find the acceleration of the particle at t = 4s. acceleration in m/s2 = My Answer s'= 012t s"= 12 acceleration in m/s2 = 12

Physics
The maximum velocity and acceleration of a particle executing SHM about its equilibrium position are 4.0m/s and 64.0m/ss respectively. If the acceleration of the particle is 64.0m/ss at t=0. Write an expression for the velocity of the particle as a

physics
Particle 1 is moving on the xaxis with an acceleration of 5.55 m/s2 in the positive xdirection. Particle 2 is moving on the yaxis with an acceleration of 7.45 m/s2 in the negative ydirection. Both particles were at rest at the origin at t = 0 s. Find

English
1.All of the balloons on the string (popped) except two. 2.Do you (want) to buy those books? 3.Daniel's dog is (following) the trail to the river's edge. 4.For thirty years the noon whistle has (blown)exactly on time. 5.The players have (challenged) their

Math
A particle starts at the origin and moves along the curve 4y = x^2 to the point (4, 4). If the ycomponent of its acceleration is always equals 2 and the ycomponent of its velocity is initially zero, find the xcomponent of its acceleration.

science
When a particle starts from rests and moves with constant acceleration then why its path is always a straight line?

physics
A particle moving with a constant acceleration describes in the last second of it's motion 9/25th of the whole distance.of it starts from rest ,how long is the particle is in motion and through what distance does it move if it describes 6cm in first

Physics
Uugghhh help please. The velocity of a 4.6 kg particle is given by vector v=(4t{i}+7t^2{j}), where v is in m/s and t is in seconds. At the instant when the net force on the particle has a magnitude of 40 N, what is the angle between the particle's

physics
Particle 1 is moving on the xaxis with an acceleration of 5.55 m/s2 in the positive xdirection. Particle 2 is moving on the yaxis with an acceleration of 7.45 m/s2 in the negative ydirection. Both particles were at rest at the origin at t = 0 s. Find

PHYSICSS!!!!!
At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi = (3.00 i  2.00 j) m/s and is at the origin. At t = 2.00 s, the particle's velocity is v = (6.60 i + 4.00 j) m/s. Find the acceleration of the particle at any time

physics
At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of vi = (3.00 i  2.00 j) m/s and is at the origin. At t = 2.00 s, the particle's velocity is v = (6.60 i + 4.00 j) m/s. Find the acceleration of the particle at any time

mt
a particle p starts from a point a with velocity 4m/s.if it is moving along a strait line ab with an acceleration of 1.5t^2 at a time t seconds, find acceleration,diplacment after ten seconds,velocity

Physics
A particle residing in one dimension is moving with constant acceleration a=4m/sec^2 .At time t =2sec, the particle is located at x=3m and is observed to have velocity v=6m/sec. (a) At what instants is the particle to be found at x=0m?(ii)what is the

math
Which three options are true about motion in a straight line. A. A particle which moves at an increasing velocity has a constant acceleration. B. If two particles always have the same velocity as each other, their separation does not change. C. A particle

Calculus AB
The position function of a particle in rectilinear motion is given by s(t) = 2t^3  21t^2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer. So I've

Math
A particle is moving at some constant speed. Use the following information to answer the following questions. s(t)=100/t©÷+12; t¡Ã0; see represents feet and t represents seconds a)Find the velocity and acceleration equations for this particle. b)When

physics
A particle moves in the xy plane with constant acceleration. At time zero, the particle is at x = 9 m, y =6 m, and has velocity vo =(4.5 m/s)i + (−4 m/s)j. The acceleration is given by a = (6 m/s2)i + (1 m/s2)j. What is the magnitude of the displacement

science
a particle travels in a straight line ,such that for a short time 2s

physics
question 1  If Rojelio starts out at rest, and in 10 s speeds up to 50 m/s, what is his acceleration? A  12 m/s^2 B  8 m/s^2 C  5 m/s^2 D  15 m/s^2 question 2  If Juan starts out at 10m/s, and in 15 s speeds up to 60 m/s, what is his acceleration? A

physics
A particle moves along the y axis according to y(t)=(3.5 m/s^2)t^2  (9.0 m/s)t + 5.0 m. (a) What is the particle's velocity as a function of time? (b) What is the particle's acceleration at t=2.0 s?

Physice
Suppose we are told that acceleration A of a particle moving with unifrom speed V circle of radios

Physics Quick!!
At t = 0, a particle moving in the xy plane with constant acceleration has a velocity of i = (3.00 i − 2.00 j) m/s and is at the origin. At t = 2.00 s, the particle's velocity is = (6.60 i + 7.00 j) m/s. (Round your coefficients to two decimal places.)