Question

A particle is moving along positive x- axis. Its position varies as x=t³-3t²+12t+20
What is the velocity of the particle when its acceleration is zero?​

Answer 1

12m/sec

Explanation:

Hey There!!!

Here we are given position as a function of time:

x = t^3-3t^2+12t+20x=t3−3t2+12t+20

Velocity is defined as the derivative of position with respect to time. So we have:

v=\frac{dx}{dt} = 3t^2-6t+12v=dtdx=3t2−6t+12

Now, we want initial velocity. Whenever we have to find "initial" quantity, we have to take t = 0.

Thus, initial velocity means velocity at t=0.

At t=0, the velocity is:

\begin{gathered}v = 0 + 0 + 12 \\ \\ \implies \boxed{v = 12 \, \, m / s}\end{gathered}v=0+0+12⟹v=12m/s

Thus, Initial Velocity is 12 m/s.