A cart 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 speed would have to be somewhere between 1.667 or 1.666 miles per minute.

add 30, 15, 5 together and you will get 50

50 is the total miles traveled

then you multiply 30 by 1.666 and you will get 49.98 but it's still not quite 50 miles

if you multiply 30 by 1.667 and you will get 50.01 but its a little over to miles

i got the 30 from the minutes traveled

anyway that's the best i got for speed