Please help me with this calculus question!

Question

A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t² + 550.

What is the velocity of the ball after 3 seconds? Include units.

Answer 1

Velocity, measured in meters per second, is the rate of change of position (it tells us how much the position of the ball changes in a given time). Determining the derivative of a function is the same as determining the rate of change of the function.

So to get the velocity after 3 seconds, first get the derivative s ' (t).

s(t) = 4.9t^2+550

Use the product rule to derive:

s'(t) = (2)(4.9)t + 0

This simplifies to s'(t) = 9.8t

Since you're solving for the velocity after 3 seconds, plug in t=3:

s'(t) = 9.8 * 3 = 29.4 m/s