A 4.80-kg particle moves along the x axis. Its position varies with time accordi

ID: 1343579 • Letter: A

Question

A 4.80-kg particle moves along the x axis. Its position varies with time according to x = t + 5.0t3, where x is in meters and t is in seconds.

A) Find the kinetic energy of the particle at any time t. (Use the following as necessary: t.)

B) Find the magnitude of the acceleration of the particle and the force acting on it at time t. (Use the following as necessary: t.)

C) Find the power being delivered to the particle at time t. (Use the following as necessary: t.)

D)Find the work done on the particle in the interval t = 0 to t = 3.70 s.

the position of the particle is,

x = t + 5.0t3

The velocity of the particle is,

v = dx/dt = 1 + 15t2

Hence, the kinetic energy of the particle at any time t is,

K = 0.5mv2 = 0.5 * 4.8 * [1 + 15t2] 2 = 2.4*[1 + 15t2 ]2

The displacement at 3.7 s is,

The acceleration of the particle is,

a = dv/dt = 30t

The force exerted on the particle is,

F = ma = 4.8 *30*t = 144 t

The power is calculated as follows:

P = K/t = 2.4*[1 + 15t2 ]2 / t = 2.4 [1+225t4 + 30t2] /t = 2.4/t + 540 t3 + 72t

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