A cyclist rides 8.0 km east for 20 minutes, then he turns and heads west for 8 minutes and 3.2 km. Finally he rides east for 16 km, which takes 40 minutes. (a) What is the final displacement of the cyclist? (b) What is his average velocity?

a) 20,8 km b) 18,353 km/h

Explanation:

We first differentiate between speed and velocity, since the later is a vector, that is besides having a value associated as speed, the direction is also a part of its meaning. Then we assume here that moving towards east is a positive direction, then the total displacement is calculated as (8km - 3.2km + 16km) = 20.8 km. Now for the average speed it is total displacement over total time used. The total time is 68 minutes that in hour is 17/15 hrs=1,1333 hrs. Then the average velocity is 20,8 km / 1,1333 hrs = 18,353 km/hrs

Displacement: 20,8 to the east.

Average velocity: 18,35 km/hour

Explanation:

In order to solve this you first have to calculate the total displacement that the cyclist rode, in this case we will use east as positive distance and west as negative:

+8 km - 3,2 km + 16 km = 20,8

Now the average velocity is the result of the displacement by the total time it took:

20,8*60/68 = 18,35 km/hr

Now we know that the average belocity would be 18,35 kilometer per hour.