APPLICATIONS OF DERIVATIVES

Kinematics in Calculus

Recall

Displacement: The straight line distance from the start of an object’s path of motion to its finish.

Velocity: The rate of change of displacement with respect to time. The first derivative of displacement w.r.t time.

Acceleration: The rate of change of velocity with respect to time. The second derivative of displacement w.r.t time.

Example #1

A model rocket is launched vertically from a launch pad. It’s displacement (in m) with respect to time (in s) is given by:

d(t) = -4.9t2 + 20t +10.

a) What is the acceleration of the rocket?b) What is the rocket’s maximum height?c) What is the impact velocity of the

rocket?