Question

A speedboat increases its speed from 14.5 m/s to 29.3 m/s in a distance of 172 m.

(a) Determine the acceleration (in m/s/s) of the speedboat.
(b) Determine the time (in s) over which this acceleration occurs.

Answer 1

a. Acceleration, a = 1.88 m/s²

b. Time, t = 7.87 seconds.

Step-by-step explanation:

Given the following data;

Initial velocity, U = 14.5m/s

Final velocity, V = 29.3m/s

Distance, S = 172m

a. To find the acceleration of the speedboat;

We would use the third equation of motion;

V² = U² + 2aS

Substituting into the formula

29.3² = 14.5² + 2a*172

858.49 = 210.25 + 344a

344a = 858.49 - 210.25

344a = 648.24

a = 648.24/344

Acceleration, a = 1.88 m/s²

b. To find the time;

We would use the first equation of motion;

V = U + at

29.3 = 14.5 + 1.88t

1.88t = 29.3 - 14.5

1.88t = 14.8

Time, t = 14.8/1.88

Time, t = 7.87 seconds.