Object at rest and fall

Question

An object starts from rest and falls under the influ- ence of gravity. Draw graphs of (a) its speed and (b) the distance it has fallen, as a function of time from t = 0 to t = 5.00 s. Ignore air resistance.

Answer 1

The equation for the speed (I'll call it velocity and denote it as "v") of the object is v = at where "a" is the acceleration and "t" is time.

For this discussion I will assume that acceleration is negative because it is pulling the object down, away from you. I will assume velocity is also negative for the same reason. And I will assume the distance traveled is also negative. You COULD assume the opposite by orienting your coordinate plane of reference the opposite way.

In this case, because acceleration is constant (on the surface of the earth), then v = -9.8t (because acceleration is -9.8 m/s²).

The equation for the distance fallen (I'll call it "y") is y = 1/2at², or, plugging in a = -9.8, y = -4.9t²

You can graph these by hand drawing the graphs or by using a graphing calculator or other graphing utility (like desmos). You will get graphs that look like these:

Note, these graphs are just sketches to show the general shapes you will get. You will need to more accurately represent these with real values between t = 0s and t = 5s