A motorboat traveling on a straight course slows down uniformly from 75km/h to 40km/h in a distance of 50m. What is the boat’s acceleration?

To find the boat's acceleration, we can use the equation for acceleration:

acceleration = (final velocity - initial velocity) / time

In this case, we are given the initial velocity (75 km/h), final velocity (40 km/h), and the distance the boat traveled (50 m). However, we are not given the time it took for the boat to slow down.

To find the time, we can use the equation for uniformly decelerated motion:

distance = (initial velocity + final velocity) / 2 * time

In this case, the distance is 50 m, the initial velocity is 75 km/h converted to m/s, and the final velocity is 40 km/h converted to m/s.

First, let's convert the velocities from km/h to m/s:

75 km/h = 75 * (1000 m / 1 km) * (1 h / 3600 s) = 20.83 m/s
40 km/h = 40 * (1000 m / 1 km) * (1 h / 3600 s) = 11.11 m/s

Now we can calculate the time using the equation for uniformly decelerated motion:

50 m = (20.83 m/s + 11.11 m/s) / 2 * time

Dividing both sides by (20.83 m/s + 11.11 m/s) / 2:

50 m = 16.97 m/s * time

Dividing both sides by 16.97 m/s:

time = 50 m / 16.97 m/s ≈ 2.95 s

Now that we have the time, we can calculate the boat's acceleration using the equation for acceleration:

acceleration = (11.11 m/s - 20.83 m/s) / 2.95 s ≈ -3.23 m/s^2

Therefore, the boat's acceleration is approximately -3.23 m/s^2, indicating that it is decelerating (slowing down).

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