Find the velocities

Question

Two particles have a position at time t given by the equations S1 = -t^3 -t and S2 = 6t^2 - t^3.

Find their velocities when they have the same acceleration.

My answer is V1 = 2 and V2 = 9. I'm not very sure of it.

Answer 1

S₁ = -t³ - t

S₂ = 6t² - t³.

Velocity is the derivative (with respect to time) of position so:

V₁ = -3t² - 1

V₂ = 12t - 3t²

Acceleration is the derivative (with respect to time) of velocity so:

A₁ = -6t

A₂ = 12 - 6t

The accelerations are the same when A₁ = A₂ so:

-6t = 12 - 6t

0 = 12

Since 0 never equals 12, there are NO values of "t" where the accelerations are equal