URGENT, Calculus!
posted by Vanessa on .
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

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.