Question

A science project studying catapults sent a projectile into the air with an initial velocity of 30 m/s. The formula for distance (s) in meters with respect to time in seconds is
s = -4.9t2 + 30t. Find the instantaneous rate of change (and thus the velocity at any time) using and then find the instantaneous rate of change at:
t = 1
t = 3

Answer 1

That formula applies only if the projectile is launched straight up. That would not be a practical way of launching an object with a catapult, unless you are doing a Monty Python movie and launching dead cows.

Unless the motion is in a straight line, as it is in this case, the rate of change of the distance away, ds/dt, is NOT the velocity.

Having said that, the rate of change of s is 30 - 9.8t m/s

Plug in t = 1 and then t=3 for the velocities they ask for.