Question

A particle of mass m moving along the x-axis experiences the net force Fx = ct, where c is a constant. The particle has velocity v0x at t = 0.

Find an algebraic expression for the particle's velocity vx at a later time t.
Express your answer in terms of the variables c, t, v0x, and m.

Answer 1

To find the particle's velocity at a later time t, we integrate the acceleration (which is Fx/m) over time, considering the initial velocity. The algebraic expression for the velocity vx at time t is vx(t) = v0x + (c/m) · (t^2/2).

Step-by-step explanation:

A particle of mass m moving along the x-axis experiences a net force Fx = ct, where c is a constant. To find the algebraic expression for the particle's velocity vx at a later time t, we can use Newton's second law of motion, which states that the net force applied to an object is equal to the mass of the object multiplied by its acceleration (F = ma).

In this case, the acceleration a as a function of time can be found by rearranging the formula to a = Fx / m. So, the acceleration at any time t is a(t) = ct / m. Since acceleration is the derivative of velocity with respect to time, the velocity can be found by integrating the acceleration over time.

The integral of a(t) from 0 to t gives vx(t) - vx(0) = (c/m) · (t2 / 2). We were given that the initial velocity at t = 0 is v0x. Therefore, the velocity at time t is vx(t) = v0x + (c/m) · (t2/2).