Question

If the distance traveled by a ball rolling down an incline in t seconds is s feet, where s = 6t2, find its speed and acceleration when t = 2.00 s.

Answer 1

The speed is given by the first derivative of the displacement wrt time, i.e.,

v = ds / dt

We're given, s = 6t², where s is in feet.

Hence,

v = d (6t²) / dt

v = 12t

At t = 2.00 s,

v = 12 × 2.00

v = 24 feet s^(-1)

Well, acceleration is constant, and is given by the first derivative of velocity, or second derivative of displacement, wrt time. So,

a = dv / dt

a = d (12t) / dt

a = 12 feet s^(-2)