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MathCalculus

What Is Rate of Change? Instantaneous vs. Average Velocity for a Dropped Ball

The ball reaches the ground after 2 seconds. Its instantaneous velocity then is −64 ft/s, while its average velocity over the fall is −32 ft/s.

Question

A ball is dropped from a height of 64 feet. Its height above ground, in feet, tt seconds later is

s(t)=−16t2+64.s(t)=-16t^2+64.
  1. What is the instantaneous velocity of the ball when it hits the ground?
  2. What is the average velocity during its fall?

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Evidence boundary

The answer uses the position model s(t)=−16t2+64s(t)=-16t^2+64 exactly as given. The velocities describe this idealized model; no additional effects such as air resistance are introduced.