A 13.00 kg particle starts from the origin at time zero. Its velocity as a funct

Question

A 13.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by where V is in meters per second and t is in seconds. (Use the following as necessary: t.) (a) Find its position as a function of time. (b) Describe its motion qualitatively. This answer has not been graded yet. (c) Find its acceleration as a function of time. m/s2 (d) Find the net force exerted on the particle as a function of time. (e) Find the net torque about the origin exerted on the particle as a function of time. N·m

Explanation / Answer

a)

Here , velocity of particle is

v = 8 t^2 i + t j

Now, position , r = integrate(v * dt)

r = (8/3) * t^3 i + t^2/2 j

b)

the particle moves in both x and y direction with increasing speeds in both x and y -direction

c)

a = dv/dt

a = d/dt(8 t^2 i + t j )

a = 16 t i + j m/s^2

d)

using second law of motion

Fnet = m *a

Fnet = 13 *(16 t i + j)

Fnet = 208 * t i + 13 j

the net force acting on the particle is 208 * t i + 13 j

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