Question

A speedboat increases in speed from 20 m/s to 30 m/s in a distance of 200m. Find (a) the magnitude of its acceleration and (b) the time it takes the boat to travel this distance.

(a) (I am not sure what the magnitude is)
(b) 200m x s/30m = 6.67s (is this correct?)

Answer 1

It's a bit easier if you do (b) first.

(b) The average speed will be 25 m/s, and the time required to travel that distance will be 200 m/(average speed) = 200m/(25 m/s) = 8 s
(a) The magnitude of the acceleration is (speed change)/time = (10 m/s)/8 s = 1.25 m/s^2

You could also have used the formula
2aX = V2^2 - V1^2 = 900 - 400 = 500, and solved for the acceleration
a = 500/(2X) = (500 m^2/s^2)/400 m. You'd get the same answer; however, that formula is a bit harder to remember.

Answer 2

1,25