Both cars - Position and velocity graphs

At what instant(s) do the two cars have the same velocity?

  1. When your car first passes the Porsche.
  2. When the Porsche passes you.
  3. At both of the above instants.
  4. At some time between 1. and 2.

4 is correct. You first pass the Porsche because you're going faster, and later the Porsche passes you because it's going faster. At some intermediate time, both cars have the same speed.

The position graph gives two points where the cars pass each other. You pass the Porsche around 1.8 s, x = 6 m, and the Porsche passes you around 5.7 s, x = 50 m.

By finding when the Porsche passes your car, we then find the Porsche's speed from v(t). At t = 5.7 s, the Porsche's speed is about 17 m/s.