Acart is pushed at a supermarket for a distance of 30 m south, then 15 m west and finally 5 m west. this entire motion lasts for 30 minutes. what was the average speed of the cart? what was the average velocity of the cart?

(how would i find the average speed and velocity? )

Let the displacement vector S be 30 m South and W 20 m West

S^2 + W^2 = D^2   where D is the magnitude of the total displacement vector

D = (30^2 + 20^2)^1/2 = 36.1 m

So the magnitude of the velocity is D / 30 = 1.20 m/min

The direction of the displacement is given by

tan theta = 20 /30 = 2/3    and theta = 33.7 deg

So the average velocity is 1.2 meter/min at 33.7 deg West of South

The average speed is 50 m / 30 min = 1.67 meter/min

the total distance traveled by the car is

30km + 49km = 79 km .