Question

A 4.60 kg particle moves along the x axis. Its position varies with time according to x = t + 1.8t³, where x is in meters and t is in seconds.

(a) Find the kinetic energy at any time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary

_______J

(b) Find the acceleration of the particle and the force acting on it at time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)

A=______m/s2

F=_______N

(c) Find the power being delivered to the particle at time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)

P=_________W

Answer 1

given equation is x = t + 1.83 t^3

Velocity V = dx/dt

V = (t + 1.8t^3)/dt

V = dt/dt + 1.8 dt^3/dt

V = 1 + 1.8 * 3 t^2

V = 1 + 5.4 t^2

Kinetic Energy U = 0.5 m v^2

U = 0.5 * m * (1 + 5.4t^2)^2

U = 0.5* 4.6 *(1+ 5.4t^2)^2

U = 2.3 *(1+ 5.4 t^2)^2 JOules

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part B :

Acceleration a = dV/dt

a = d(1 + 5.4t^2)/dt

a = 0 + 5.4 *2* t

a 10.8 t m/s^2

Force F = m a

F = 4.6 * 10.8 t

F = 49.68 t Newtons
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POwer = force * velocity

P = 49.68 t * (1 + 5.4t^2)

P = 49.68 t + 268.27 t^3 Watts