At time t, in seconds, the position, in meters, of a particle moving along the x-axis is x(t)=t3−4t. Assume for all parts of this problem that t≥0.

Question

 Find the particle's acceleration whenever the velocity is zero

Find the velocity of the particle whenever the acceleration is zero

Answer 1

So x(t) = t³ - 4t.

Taking the derivative once, gives the velocity v(t) = 3t² - 4.

For the acceleration, take the derivative one more time, a(t) = 6t

Setting the velocity equation equal to zero gives 3t² = 4 and so velocity is zero at t = 2/√3. The acceleration at this time is 6*2/√3.

The acceleration is zero only at t = 0. The velocity at this time is -4