Question

a cyclist travels 30 km north and then 40 km east in a total of 2 hours. what is the difference between the cyclists average speed and the magnitude of their average velocity?
options:
25 km/h
35 km/h
10 km/h
50 km/h

Explanation:

Step1: Calculate total distance

Total distance \(d = 30+40=70\) km.

Step2: Calculate average speed

Average speed \(v=\frac{d}{t}\), where \(t = 2\) hours. So \(v=\frac{70}{2}=35\) km/h.

Step3: Calculate displacement

Using Pythagorean theorem, displacement \(s=\sqrt{30^{2}+40^{2}}=\sqrt{900 + 1600}=\sqrt{2500}=50\) km.

Step4: Calculate average velocity

Average velocity \(V=\frac{s}{t}\), \(t = 2\) hours. So \(V=\frac{50}{2}=25\) km/h.

Answer:

Average speed: \(35\) km/h; Average velocity: \(25\) km/h.