A speedboat increases its speed uniformly from 20 m/s to 32 m/s in a distance of 240 m.

(a) Find the magnitude of its acceleration.
?m/s2
(b) Find the time it takes the boat to travel the 240 m distance.
?s

To find the magnitude of acceleration, we can use the formula:

acceleration (a) = change in velocity (Δv) / time taken (Δt)

We have the initial velocity (u) as 20 m/s and the final velocity (v) as 32 m/s. The change in velocity is the difference between the final and initial velocities:

Δv = v - u = 32 m/s - 20 m/s = 12 m/s

We also know the distance (s) covered by the boat, which is 240 m. Using the formula for average velocity:

average velocity (v_avg) = total distance (s) / total time (t)

Since the boat is accelerating uniformly, the average velocity is simply the average of the initial and final velocities:

v_avg = (u + v) / 2 = (20 m/s + 32 m/s) / 2 = 52 m/s / 2 = 26 m/s

We can rearrange the formula to solve for time:

total time (t) = total distance (s) / average velocity (v_avg)

t = 240 m / 26 m/s ≈ 9.23 s

Therefore, it takes approximately 9.23 seconds for the boat to travel the 240 m distance.

Now, to find the magnitude of acceleration:

a = Δv / Δt = 12 m/s / 9.23 s ≈ 1.30 m/s²

So, the magnitude of its acceleration is approximately 1.30 m/s².