# Consider a car driven along a circular racetrack of radius 1.6 km. What is the magnitude of its displacement after 2.5 laps? What is the total distance traveled?

Nov 18, 2015

$\text{3.2 km}$

#### Explanation:

A circular track of radius $\text{1.6 km}$ has a diameter of $\text{3.2 km}$ ($D = 2 r$) and a circumference (distance around) of $\text{10.05 km}$. ($C = \pi \times D$)

The displacement after one lap is zero, since displacement is a vector quantity, requiring both magnitude (size) and direction away from the original position. You're back where you started, so displacement is zero.

The same applies after two laps.

The next half a lap takes the car to the exact opposite side of the track, or one diameter from its start position, $\text{3.2 km}$ away.