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Question

A particle is moving on the x-axis. The velocity of the particle increases with x as v=v0+kx. Which of the following is true about the acceleration of the particle?
  1. Acceleration is zero
  2. Acceleration is constant but non-zero
  3. Acceleration increases with time
  4. Acceleration decreases with time.


Solution

The correct option is C Acceleration increases with time
Differentiate v=vo+kx with time to get the acceleration
a=dvdt=kdxdt=k(vo+kx)
We need to find x(t) to get time dependence of acceleration a.
Re-write given expression of v as dx=(vok+x)kdt and integrate (let the particle start from the origin)
xodxvok+x=ktodt
We get x=vok(ekt1)
Substitute x in the expression of a to get a=vokekt
Hence, we can say that acceleration of the particle increasing with time.

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