Question

a circular test track for cars has a circumference of 3.7 km. a car travels around the track from the southernmost point to the northernmost point.

part a
what distance does the car travel?
express your answer with the appropriate units.

distance = value units

submit request answer

part b
what is the cars displacement from its original position?
express your answer with the appropriate units.

d = value units

submit request answer

Explanation:

Step1: Recall distance formula for semi - circle

The car travels from the southernmost to the northernmost point of a circular track, which is half - circle. The distance $d_{1}$ traveled is half of the circumference $C$ of the circle. Given $C = 3.7$ km.
$d_{1}=\frac{C}{2}$

Step2: Calculate the distance

Substitute $C = 3.7$ km into the formula.
$d_{1}=\frac{3.7}{2}=1.85$ km

Step3: Recall displacement concept

Displacement is the straight - line distance from the initial to the final position. For a car moving from the southernmost to the northernmost point of a circular track, the displacement $d_{2}$ is equal to the diameter $D$ of the circle. Since $C=\pi D$, then $D=\frac{C}{\pi}$.
$D=\frac{3.7}{\pi}\approx1.18$ km

Answer:

Part A:
distance = 1.85 km
Part B:
d = 1.18 km