Question

A particle of mass m moving along the x-axis experiences the net force F ct, where c is a constant. The particle has velocity algebraic expression for the particle's velocity Vox at t 0. Find an V at a later time t.

Answer 1

The velocity of a particle of mass m moving under a time-varying force F = ct can be found by integrating the force over time, resulting in the velocity equation (c/2)t² + V0x for a later time t.

Step-by-step explanation:

The question asks about a particle of mass m moving along the x-axis under the influence of a net force that varies with time (F = ct, where c is a constant). Given that the particle has an initial velocity V0x at t = 0, we need to find the particle's velocity at a later time t.

To find the velocity at a later time t, we use the fact that force is the rate of change of momentum. Since the force varies with time, we integrate the force over time to get the change in momentum, and thus the change in velocity. According to Newton's second law,

F = ma = m(dv/dt)

For a force that varies with time as F = ct, we can integrate this expression:

∫ F dt = ∫ m dv

Integrating both sides,

ct dt = m dv,

which gives us

(c/2)t² + V0x = v.

So, the velocity at time t is (c/2)t² + V0x.