Question

If a body moves in a straight line according to the law s = 24t + 3t^2 - t^3, where s is the distance measured in meters from the origin and t is the time in seconds after it starts to move, calculate the body's velocity as a function of time.
A. 63 m/s
B. 15 m/s
C. 27 m/s
D. 81 m/s

Answer 1

As the comments state, the velocity is the derivative of the position.

Therefore, the velocity as function of time is:

ds / dt = 24 + 6t - 3t^2.

That is a parabola whose maximum is (1,27). With that you know that the velocity will never be either 63 m/s or 81 m/s.

Also, you know that the velocity at t = 1 s is 27 m/s.

And, you can also find that the velocity at t = 3 is 15 m/s.

I am confident on that this analysis solves your question. Else, insert a comment.