A speedboat travels in a straight line and increases in speed uniformly from v i

Question

A speedboat travels in a straight line and increases in speed uniformly from vi = 16.0 m/s to vf = 45.5 m/s in a displacement %u0394x of 210 m. We wish to find the time interval required for the boat to move through this displacement.

(c) vf2 = vi2 + 2a%u0394x

(d) Solve the equation selected in part (c) symbolically for the boat's acceleration in terms of vi, vf, and %u0394x

(e) Substitute numerical values to obtain the acceleration numerically

(f) Find the time interval mentioned above

please i need clear answer thanks

Explanation / Answer

initial velocity (u) = 20
final velocity (v) = 30
distance (s) = 200

Now we can apply an equation of straight line motion:
v^2 = u^2 + 2as
The only thing we don't know is acceleration 'a'.
30^2 = 20^2 + 2(a)(200)
900 = 400 + 400a
500 = 400a
a = 1.25 ms^(-2)

To find the time we'll use another equation for straight line motion:
v = u +at
30 = 20 + 1.25t
10 = 1.25t
t = 8 seconds

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