A ball is rolled, travelling 10 m north in 5s, then 10 m east in 10s. What is the total distance and average speed of the ball? What is the total displacement and average velocity of the ball?

First to note is how average speed, v, distance, d, and time, t, are related. This is given by v = d/t. The journey is split into two parts, but we are only asked for the total distance and average speed. It is clear that the total distance is given by 10m + 10m = 20m, from the first and second parts of the journey. The total time is t = 5s + 10s = 15 s. Hence v = 20/15 = 1.33 m/s. The total displacement can be determined by drawing a triangle of the path travelled. Using Pythagoras Theorem one can determine that the displacement, D, is D = the square root of(10^2+10^2 = 200)= 14.1 m north-east. The velocity, V, is then given by V = D/t, similar to how distance and speed are related. So V = 14.1/15 = 0.94 m/s north-east. Importantly the direction are required for displacement and velocity as they are vectors.