Question

A rock thrown vertically upward from the surface of the moon at a velocity of 32 meters per reaches a height of s(t)=32t−0.8t² meters in t seconds. a. Find the rock's velocity and acceleration as function of time.

Answer 1

The rock's velocity is given by v(t) = 32 - 1.6t and its acceleration is -1.6 m/s^2.

Step-by-step explanation:

The velocity of the rock can be found by taking the derivative of the height function with respect to time. In this case, the height function is s(t) = 32t - 0.8t^2. So, taking the derivative, we get v(t) = 32 - 1.6t. Therefore, the rock's velocity as a function of time is v(t) = 32 - 1.6t.

The acceleration of the rock can be found by taking the derivative of the velocity function with respect to time. So, taking the derivative of v(t) = 32 - 1.6t, we get a(t) = -1.6. Therefore, the rock's acceleration is constant and equal to -1.6 m/s^2.