A cyclist leaves home and rides due east for a distance of 45km. She returns home on the same bike path. If the entire trip takes 4h, what is her average speed? What is her displacement?

The return trip of the cyclist in quest 13 took 30 min longer than her trip east, although her total time was still 4h. What was her velocity in each direction?

We only help with homework, we do not provide direct answers. Have you made any attempts on this work? If so, please post what you have tried so far.

If not, let's start with displacement. Displacement is the shortest distance between your starting point and your ending point and should also show direction.

So for example, if you start at, say, Point A, and travel 10 meters East, then your displacement is 10 meters East.

If you start at Point A, travel 10 meters East, then 10 meters North. Your displacement is not 20 meters, and it is not 10 meters. Your displacement is (sqrt(200)) 14.1 meters North-East.

This is by use of the Pythagorean theory (a^2 + b^2 = c^2). It helps to draw it out.

So what is the displacement in your question?

Also, average speed is given by total distance covered divided by the total time taken.

For the second part of your question, assign a variable to the initial velocity and form equations to solve! Remember

Speed = \frac{Distance}{Time}