Graphs

A graph is basically a picture of an equation. Graphs of an object's position, velocity, and acceleration as a function of time can tell you a great deal:

Car 1 - Position and velocity graphs

Predict what the position and velocity graphs look like for the red car, which has a constant velocity of 11.11 m/s.

Note that:

Car 1 - Velocity and acceleration graphs

Predict what the acceleration graph looks like for the red car, which has a constant velocity of 11.11 m/s.

Note that:

Car 2 - Position and velocity graphs

Predict what the position and velocity graphs look like for the black car, which has a constant acceleration of 3 m/s2 starting from rest.

Note that:

Car 2 - Velocity and acceleration graphs

Predict what the acceleration graph looks like for the black car, which has a constant acceleration of 3 m/s2.

Note that:

Both cars - Position and velocity graphs

Looking at the graphs for both cars at once can actually give us the answers to the sample problem we did earlier. This is another good way to check the answers.

The position graph shows that there are two locations where the cars pass each other. The red car passes the black one around 1.8 s, at x = 6 m, and the black one passes the red one around 5.7 s, at x = 50 m. This confirms our hard work earlier, solving the quadratic.

Finding the time when the black car passes the red one, you can then figure out how fast the black car is going at that time by reading it directly off the velocity graph. At t = 5.7 s, the black car's speed is about 17 m/s, about 50% more than the red car's speed at that time.