# Physics-Trajectory

A particle's trajectory is described by x =(12t3−2t2)m and y =(12t2−2t)m, where t is in s.

What is the particle's speed at t=0s ?

What is the particle's speed at t=5.0s ?

What is the particle's direction of motion, measured as an angle from the x-axis, at t=0 s ?

What is the particle's direction of motion, measured as an angle from the x-axis, at t=5.0s ?

1. 👍 0
2. 👎 0
3. 👁 2,522
1. A. Speed = 0.

B. X = 12*5^3 - 2*5^2 =
Y = 12*5^2 - 2*5 =
Speed = sqrt(X^2 + Y^2) =

C.

D. Tan A = Y/X.
A = ?

1. 👍 0
2. 👎 9
2. Henry’s post is incorrect. Instinctively, it might be easier to just plug in the values for t, but in order to find speed from a position equation, you must take the derivative.

V(x) = x ‘(t)
V(y) = y ‘(t)

Then take the magnitude of both components. It may help to draw this on a graph, perhaps a position-time graph and / or velocity-time graph.

1. 👍 1
2. 👎 0
3. Plug it in

1. 👍 0
2. 👎 3
4. A. v=2m/s
C. -90

1. 👍 3
2. 👎 0
5. B. 17.75
Because

sqrt([3/ 2 t^2 - 4t]^2 + [t - 2]^2).

1. 👍 3
2. 👎 0
6. x =(1/2t^3−2t^2)m and y =(1/2t^2−2t)m

1. 👍 0
2. 👎 0

## Similar Questions

1. ### math

Consider a particle moving along the x-axis 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 − 9, 0 ≤ t ≤ 10 Find the open t-intervals on

asked by Anonymous on January 12, 2019
2. ### Physics

Figure (a) shows charged particles 1 and 2 that are fixed in place on an x axis. Particle 1 has a charge with a magnitude of |q1| = 12.0e. Particle 3 of charge q3 = +13.0e is initially on the x axis near particle 2. Then particle

asked by Phil on January 20, 2012
3. ### physics

Two forces, 1 = (3.85 − 2.85) N and 2 = (2.95 − 3.65) N, act on a particle of mass 2.10 kg that is initially at rest at coordinates (−2.30 m, −3.60 m). (a) What are the components of the particle's velocity at t = 11.8 s?

asked by Anonymous on March 7, 2014
4. ### 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 = 2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vy = 50 m/s, vx = vz = 0,

asked by Mary on April 29, 2015
1. ### 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

asked by sarah on November 3, 2008
2. ### College Physics

particle 1 of charge q1 = 1.04 ìC and particle 2 of charge q2 = -2.99 ìC, are held at separation L = 10.8 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from

asked by Stephanie13 on July 6, 2012
3. ### Calculus

A particle travels along the x-axis so that its velocity is given by v(t)=cos3x for 0

asked by Dalton on January 10, 2012
4. ### Physics

The position of a particle moving along the x axis is given by x= 12t2 -2t ,where x is in meters and t in seconds . determine the velocity and the acceleration of the particle at t=3.0s

asked by St on March 19, 2020
1. ### Calculus

The position of a particle moving along the x-axis is given by s(t)=2t2+4. Use difference quotients to find the velocity v(t) and acceleration a(t), filling in the following expressions as you do so: v(t)=limh->0 [_____ / h ] =

asked by Cecille on February 22, 2011
2. ### AP PHYSICS MECH.

A simple pendulum, consists of an object suspended by a string. The object is assumed to be a particle. The string, with its top end fixed, has negligible mass and does not stretch. In the absence of air friction, the system

asked by vm on January 6, 2011
3. ### 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

asked by kim on April 26, 2010
4. ### 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

asked by Aparna on January 27, 2013