Question

an astronaut drops a rock into a crater on the moon. the distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t) = 0.8t^2. what is the average speed in meters per second, of the rock between 5 and 10 seconds after

Answer 1

Given the distance function d(t) = 0.8t^2, we must derive the formula to get the formula for velocity. The first derivative of a distance function gives the velocity because it shows how the variable (distance) changes over a another variable which is usually time. Following the same line of thought, the second derivative gives the acceleration.

dt = 2(0.8)t = 1.6t = 1.6(10) - 1.6(5) = 8 m/s