# A particle moves in a straight line so that its position (x cm) from a fixed point O at time (t seconds) is given by x= t^3-6t^2-15t-5 Find the average speed of the particle in the first 7 seconds

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1. ## physics

the motion of a particle along a straight line is described by the function x=(2t-3)^2 where x is in metres and t is in seconds. A)find the position ,veocity and acceleration at t=2 sec. B) find the velocity of the particle at origin.

2. ## Physics

A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration for the particle at

3. ## math(mechanics)

the velocity of a particle traveling in a straight line is given by v=(6t-3t^2)m/s, where t is in seconds, if s=0 when t= 0. determine the particles deceleration and position when t=3s. how far has the particle traveled during the 3s time interval and what

4. ## Physics

A positively charged particle is fixed in place, unable to move. Another positively charged particle is brought near and released. (a) Which way does it move? (b) What happens to the force, acceleration, and velocity on the moving particle as it moves? (c)

5. ## AP CALC. AB

A particle moves along a line so that at time t, where 0

6. ## math

A particle moves on a straight line. The velocity after t seconds is given by V= 3t^2 – 6t – 8. The distance of the particle from the origin after one second is 1o meters. Calculate the distance of the particle from the origin after 2 seconds.

7. ## AP Calculus

A particle is moving along a horizontal straight line. The graph of the position function (the distance to the right of a fixed point as a function of time) is shown below. Answer the following questions only on the interval (0,8). 1. When is the particle

8. ## Quantum Physics

Consider a particle whose wavefunction at some fixed time t is represented by -A if -2≤x≤0 ψ(x)= A if 0≤x≤3 0 otherwise (a) What is the normalization constant A? (b) What is the probability of finding the particle at a position x≤0? (c) What is

9. ## physics

positively charged particle is fixed in place, unable to move. Another positively charged particle is brought near and released. (___/ 5) (a) Which way does it move? (b) What happens to the force, acceleration, and velocity on the moving particle as it

10. ## math

For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle in intervals [0,1]

11. ## calc

Given the position function, s of t equals negative t cubed divided by 3 plus 13 times t squared divided by 2 minus 30 times t, between t = 0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle

12. ## math

A particle moves in the xy-plane so that its position for t ≥ 0 is given by the parametric equations x = ln (t + 1) and y = k(t^2) , where k is a positive constant. The line tangent to the particle’s path at the point where t = 3 has slope 8. What is

13. ## math(mechanics)

the acceleration of a particle as it moves along a straight line is given by a=(2t-1)m/s^2, where t is in seconds.if s=1m and v= 2m/s when t=0,determine the particles velocity and position when t=6s. Also, determine the total distance the particle travels

14. ## Calculus

A particle moves on a line away from its initial position so that after t hours it is s = 6t2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer. I started by taking the

15. ## Calculus

Given the position function, s(t)= (-t^3/3)+(13t^2 /2)-30t, between t=0 and t = 9, where s is given in feet and t is measured in seconds, find the interval in seconds where the particle is moving to the right. a) 3 < t < 9 b) 5 < t < 9 c) the particle

16. ## Math

A particle moves along a straight line with a velocity, v m s-1, given by v =4-8sin2t, where t is the time in seconds after passing a fixed point O. Determine the range of values of v

17. ## Calculus

A particle moves on a vertical line. Its position, s, in metres at t seconds is given by s(t) = t^3 - 9t^2 + 24t, t>0/ I found the velocity and acceleration functions. s'(t) = 3t^2 - 18t + 24 s''(t) = 6t-18 b) When is the particle moving up? down? c) Find

18. ## Calculus

A particle moves along a line so that at any time t its position is given by x(t)=2(pi)t+cos(2(pi)t). Determine the particle's maximum velocity.

19. ## physics

A moving particle encounters an external electric field that decreases its kinetic energy from 9100 eV to 6630 eV as the particle moves from position A to position B. The electric potential at A is -59.5 V, and the electric potential at B is +26.1 V.

20. ## 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

a particle moves in a straight line so that t seconds after passing a fixed point O its acceleration a cm per second is given by a=4t-16. It passes O with a velocity of 30cm per second. Find an expression for the velocity of the psrticle in terms of t and

22. ## calculus

A particle moves in a straight line with velocity given by v(t) =sin t metres per second. Find the total distance travelled by the particle in the first 4 seconds of motion

23. ## AP CALC. AB

1.The position of a particle moving on the line y = 2 is given by x(t)= 2t^3-13t^2+22t-5 where t is time in seconds. When is the particle at rest? a. t =0.268, 2.500, and 3.732 b. t = 0, 1.153, and 3.180 c. t = 1.153, 2.167 and 3.180 d. t = 2.167 e. t =

24. ## physics

A particle moves in a straight line with an acceleration a ms^-2 at time 't' seconds where a = - 1/t² when t=1 the particle has a velocity of 3ms^-1 then find the velocity when t=4

25. ## Physics

A particle moves along the x axis. It is initially at the position 0.350 m, moving with velocity 0.110 m/s and acceleration -0.380 m/s2. Suppose it moves with constant acceleration for 3.50 s. (a) Find the position of the particle after this time. (b) Find

26. ## Calculus

A particle, initially at rest, moves along the x-axis such that its acceleration at time t>0 is given by a(t)=cos(t). At the time t=0, its position is x=3. How do I find the position function for the particle? I tried integrating the equation but got

27. ## physics

A particle moves along a straight line such that its position is defined by s = (t3 – 3 t2 + 2 ) m. Determine the velocity of the particle when t = 4 s.

28. ## physics

A particle moves along a straight path through displacement i = (2.2 m) + c while force = (3.2 N) - (3.8 N) acts on it. (Other forces also act on the particle.) What is the value of c if the work done by on the particle is (a) zero, (b) 3.2 J, and (c) -7.3

29. ## 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=2t-t^2. given that particle comes instantanuously at rest at p. Find i) time taken to reach p? ii) the acceleration at p? iii) distance

30. ## Physics

A particle moves in a straight line so that its position (x cm) from a fixed point O at time (t seconds) is given by x= t^3-6t^2-15t-5 Find the average speed of the particle in the first 7 seconds

31. ## Maths, dynamics

A particle of mass 45 kg moves in a straight line such that the force (in Newtons) acting on it at time t (in seconds) is given by 225t^4-90 t^2-225. If at time t = 0 its velocity, v , is given by v ( 0 ) = 2, and its position x (in m) is given by x ( 0 )

32. ## mathematics : intergration

A particle moves in a straight line through a fixed point O with a velocity (4-t)m/s find an expression for its displacement S from this point given that S=S when t=0

33. ## calculus

A particle p moves in a straight line with a velocity v m/sec that is given by v=4t^2-1 where t is the time after passing through a fixed point O on the line .find the instant when p is instantaneously at rest .also find at that instant ,displacement of p

34. ## Calculus

a particle moves along the x-axis at a velocity of v(t)=1 sqrt(t), t>0. at time t=1 , its position is x=4. find the acceleration and position functions for the particle

35. ## Calculus

A particle moves in a straight line under a force such that its displacement s(t), in metres, at time t seconds, is given by s(t) = t3 − 5t2 + 3t +15 (i) Find the expression for the velocity of the particle. (ii) Find the time at which the particle is at

a particle moves in a straight line such that its position x from a fixed point 0 at time 't' is given by x= 5 + 8sin2t + 6cos2t 1. Find the period and amplitude of the particle. 2. Find the greatest speed of the particle. Could you please explain the

37. ## Dynamics

The acceleration of a perticle as it moves along a straight line is geven by a=(2t-1) m/s2. If x=1m and v=2m/s when t=0s, determine the particle's velocity and position when t=6s. Also, determine the total distance the particle travels during this time

38. ## Math

A particle moves along a straight line with a velocity, v ms/s, given by v = 4 - 8 sin 2t where t is the time in seconds after passing a fixed point O. 1. Determine the range of values of v.

39. ## Ap Calculus

Please help. A particle moves in a stright line and its acceleration is given by a(t)=6t+4. its initial position is s(0)=9 and its position when t=1 is s(1)=6. find the velocity of the particle when t=2. A. v(2)=14 B. v(2)=7 C. v(2)=4 D. v(2)=9 E. v(2)=0

40. ## Calculus

How would I solve this: -A particle moves along a line so that, at time t, its position is s(t)=8 sin2t. a) For what values of t does the particle change direction? b) What is the particle's maximum velocity?

41. ## 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

42. ## physics

A moving particle encounters an external electric field that decreases its kinetic energy from 9530 eV to 7800 eV as the particle moves from position A to position B. The electric potential at A is -69.0 V, and that at B is +39.0 V. Determine the charge of

43. ## physics

A particle moves along the x axis. It is initially at the position 0.280 m, moving with velocity 0.080 m/s and acceleration -0.240 m/s2. Suppose it moves with constant acceleration for 3.10 s. (a) Find the position of the particle after this time. (b) Find

44. ## Math

a particle moves along x-axis so that its position at any t>=0 is given by x=arctant. What is the limiting position of the particle as t approaches infinity?

45. ## physics

A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = -5.5 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vx = 50 m/s, vy = vz =

46. ## Physics

The position of a particle moves along the equation X = Vo/K (1 - e^(-KT)) Vo and K are constants a)determine the total distance that the particle moves b) Show that the aceleration is derived from the velocity c) Reason how it could take an infinite

47. ## kinematics

these are two similar kinematics maths question which i don't know. Please help! 1)A particle moves in a straight line so that its distance, s metres, from a fixed point O is given by s = 2t^3 - 3t^2 - 12t + 6, where t is the time in seconds after passing

48. ## Mathematics

a particle moves in a straight line such that its position x from a fixed point 0 at time 't' is given by x= 5 + 8sin2t + 6cos2t 1. Find the period and amplitude of the particle. 2. Find the greatest speed of the particle. Thanks

49. ## math

For 4.95 seconds , a particle moves in a straight line according to the position function: s(t) = e^t(5-t)-5 . a. when id the particle at rest ? when is particle moving forward ? b. Find the total distance traveled by the particle in intervals [0,1]

50. ## maths

A particle of mass 40 40kg moves in a straight line such that the force (in newtons) acting on it at time,t (in seconds) is given by, 160t^4-320t^2-360 at time t=0, v is given by v(0)=10, and its position x is given by x(0)=14. What is the position of the

51. ## physics

A particle is moving along a straight line and its position is given by the relation x=( t3-6t2-15t+40)mm. Find:- (a). The time at which velocity is zero. (b). Position & displacement of the particle at that point. (c). Acceleration for the particle at

52. ## physics

A particle is moving along a straight line and its position is given by the relation x=(t3- 6t2- 15t+40) m FIND a) The time at which velocity is Zero, b) Position and displacement of the particle at that point. c) Acceleration for the particle at that

53. ## math(mechanics)

a particle moves along a straight line such that its position is defined by s=(t^2-3t^2=2)m.determine the average velocity, the average speed, and the acceleration of the particle when t=4s.

54. ## 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

55. ## 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

56. ## mathematics :integration

A particle moves in a straight line through a fixed point O with velocity (4-t)m/s find an expression for its displacement S from this point given that S=5 when t=0

57. ## calculus

a particle moves along a number line measured in cm so that its position at time t sec is given by s=72/(t+2) +k, k is a constant and t>=0 seconds. (a) Find the instantaneous velocity of the particle at t=4 seconds (b) Find the acceleration of the particle

58. ## 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

59. ## Quick calc question

A particle moves on a line away from its initial position so that after t hours it is s = 4t^2 + t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

60. ## math

A particle moves on a line away from its initial position so that after t hours it is s = 6t2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

61. ## math

A particle is traveling along a one-dimensional 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.

62. ## physics # 1

1. If a particle moves in a plane so that its position is described by the function x = Acosùt, and y = Asinùt, it is a.) moving with varying speed along a circle b.) moving with constant speed along a circle c.) moving with constant acceleration along a

63. ## calculus

A particle moves along a horizontal line such that its position s(t) = (t^2e^3t/3)for time t. Find when the particle is at rest.

64. ## calculus

A particle traces the path vector r = (t^3, t+3, t^2 -4t) where t represents time; it flies off on a tangent when t=1 and then moves in a straight line with constant speed. Find its position when t=4. Do I just plug the 4 into the t's in vector r?

65. ## physics

a particle with velocity of 2m/s at t= 0 moves along a straight line with constant acceleration of 0.2m/s2. find the displacement of the particle in 10 seconds

66. ## maths

A particle with a velocity of 2m / s at t = 0 moves along a straight line with a constant acceleration of 0.2m / s s.find the displacement of the particle in10 second

67. ## dynamic

A particle moves along a straight line with an acceleration of m/s2, where s is in meters. Determine the particle’s velocity when s = 2m, if it start from rest when s = 1m.

68. ## physics

A 8.72 kg particle moves from the origin to position C , having coordinates x = 2.04 m and y = 2.04 m as shown in Figure 1. A particle moving in a horizontal plane from the origin to position C experiences a friction force with constant magnitude 2.32 N.

69. ## Physics

F=6kt This force acts on a particle of mass "m" that moves along a line. If the particle starts from rest, determine its velocity and position at time t.

70. ## Maths

A particle moves on a line away from its initial position so that after t hours it is s=3t^2+t miles from its original position.

71. ## physics,dynamics

The acceleration of a particle along a straight line is defined by a = (2t - 9) m/s2, where t is in seconds. At t = 0, s = 1 m and v = 10 m/s. When t = 9 s, determine (a) the particle’s position, (b) the total distance traveled, and (c) the velocity.

72. ## Calc

A particle moves along the x-axis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3 - 3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for which the particle is

73. ## Calc

A particle moves along the x-axis in such a way that it's position in time t for t is greator or equal to 0 is given by x= 1/3t^3 - 3t^2 +8 A) show that at time t= 0 the particle is moving to the right. B) find all values of t for which the particle is

74. ## physics

A particle leaves the origin with an initial velocity = (2.35 m/s) and moves with constant acceleration = (-1.90 m/s2) + (2.60 m/s2)>. (a) How far does the particle move in the x direction before turning around? m (b) What is the particle's velocity at

75. ## calculus

A particle moves on the x-axis so that its velocity at any time t is given by v(t) = sin 2t. At t = 0, the particle is at the origin. a)For 0 ≤ t ≤ π, find all values of t for which the particle is moving to the left. b)Write an expression for the

76. ## physics

A particle with a charge 7C and a mass of 20kg is traveling in a circular path around a fixed particle of charde -5C. The velocity is observed to be 3000m/sec. A 9C particle with the same velocity is instead in the presence of a uniform electric field of

77. ## calculus

A particle moves in a straight line under a force such that its displacement s(t), in metres, at time t seconds, is given by s(t) = t3 − 5t2 + 3t +15 Find the time at which the particle is at rest?

78. ## calculus

Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t

79. ## Physics

A moving particle encounters an external electric field that decreases its kinetic energy from 9160 eV to 7160 eV as the particle moves from position A to position B. The electric potential at A is -58.0 V, and that at B is +22.0 V. Determine the charge of

80. ## physics

A movig particle encounters an external electric field that decreases its kinetic energy from 9670 eV to 7540 eV as the particle moves from position A to position B. The electric potential at A is -66.0 V, and that at B is +16.0 V. Determine the charge of

81. ## calc-kinematics

if a particle moves along a line so that at time t where t [0,pi] its position is given by s(t)=-4cost-t^2/2+10 what is the velocity of the particle when its acceleration is zero? so i found v(t) = 4sint-t a(t)=4cost-1 = 0 solved for t plugged it into v(t)

82. ## Physics 2

A particle moves along a line where the potential energy of its system depends on its position r as graphed in Figure P8.46. In the limit as r increases without bound, U(r) approaches +1 J. (a) Identify each equilibrium position for this particle. Indicate

83. ## calculus

a particle starts from rest and moves along a straight line with an acceleration equal to 24-15√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

84. ## calculus

a particle starts from rest and moves along a straight line with an acceleration equal to 24-15√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?

85. ## calculus

a particle starts from rest and moves along a straight line with an acceleration equal to 24-15√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?

86. ## physics

how is the position of a particle moving along a straight line described by a number

87. ## ap calculus

A particle moves along a straight line with displacement s(t), velocity v(t), and acceleration a(t). Show that a(t) = v(t) dv/ds.

88. ## math

a particle M oscillators (that is, moves back and forth) in a straight line along the horizontal axis. the position of M is given by: s(t) = 4 + 2 sin(2t) (1) Find the velocity (v) and acceleration (a) functions. (2) Find the initial position, initial

89. ## science

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

90. ## Calculous

A particle moves along the c-axis so that at time t its position is given by x(t)=t^2-6^t+9t+11 a)What is the velocity of the particle at t=0 b)During what time intervals is the particle moving to the left? c)What is the total distance traveled by the

91. ## physics

A particle moves from rest, its initial position being given by x = c with reference to a fixed point O. Its acceleration at a distance ‘x’ from 0 is mu/x^2 away from O. Show that its velocity is sqrt mu/c when it is a distance ‘x’ from O.

92. ## Calculus

a particle moves along a line so that at any time t its position is given by x(t)=2(pi)t + cos2(pi)t find velocity find acceleration what are the values of t, 0

93. ## physics

Our teacher want us to use integrate and use the dot method to solve for this question but I don't know how. Can any turor help me.A particle moves in the xy plane (see the figure below) from the origin to a point having coordinates x = 7m and y = 5m under

94. ## physics

A moving particle encounters an external electric field that decreases its kinetic energy from 9100 eV to 6630 eV as the particle moves from position A to position B. The electric potential at A is -59.5 V, and the electric potential at B is +26.1 V.

95. ## calculus

A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed when t = 9. f(t) = t ^-1 - t

96. ## Physics

A pendulum consist of a particle P of mass m, attached to one end of a model string of length l=2.85m. The other end of the string is attached to a fixed point O and the particle moves in a vertical circle about the fixed point. The angle made by the

97. ## 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

98. ## calculus

A particle moves on a line away from its initial position so that after t hours it is s = 6t^2 + 2t miles from its initial position. Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.