For free fall near the surface of a planet where the acceleration due to gravity has a constant magnitude of g length-units/sec², Equation (1) in Exercise 125 takes the form

where s is the body’s height above the surface. The equation has a minus sign because the acceleration acts downward, in the direction of decreasing s. The velocity v₀ is positive if the object is rising at time t = 0 and negative if the object is falling. Instead of using the result of Exercise 125, you can derive Equation (2) directly by solving an appropriate initial value problem. What initial value problem? Solve it to be sure you have the right one, explaining the solution steps as you go along.

Exercise 125

The standard equation for the position s of a body moving with a constant acceleration a along a coordinate line is

where v₀ and s₀ are the body’s velocity and position at time t = 0. Derive this equation by solving the initial value problem

Transcribed Image Text:

=1281² 2gt² + vot + So. S = (2) in