### Home > CALC > Chapter 6 > Lesson 6.1.3 > Problem 6-39

VERTICAL MOTION

The acceleration due to gravity is a constant near the surface of the Earth. Its accepted values are or

. These values are all the information needed to derive the equations

*and*

*for vertical motion for any dropped or thrown object.*

Describe how can you find a velocity function when given the acceleration function.

Acceleration is the rate of change of velocity...

Find

ifft/secand if the initial velocity of an object,, isfeet per second. There is a relationship between the

and the initial velocity. Find its height

if the starting position of the object,, isfeet above ground. Velocity is the rate of change of position...

Find the velocity of the object when it hits the ground.

First find the TIME when the object hits the ground:

.Then evaluateat that time.Find the maximum height attained by the object.

Find the vertex of the position function. You could use Algebra or Calculus.

At what time is the object's speed greatest?

Where is the slope of

the steepest? Remember that speed is the absolute value of velocity.