Question

A boat is cruising in a straight line at a constant speed of 2.2 m/s when it is shifted into neutral. After coasting 10 m, the engine is engaged again, and the boat resumes cruising at the reduced constant speed of 1.2 m/s. Assuming constant acceleration while coasting, how long did it take for the boat to coast the 10 m?

Answer 1

To find the time the boat coasted for 10 m, kinematic equations are applied using the initial speed, displacement, and the fact that it stopped moving (final speed zero). The acceleration is calculated first, which is then used to determine the time taken.

Step-by-step explanation:

To calculate how long it took for the boat to coast the 10 m, we need to use kinematic equations that relate displacement, initial velocity, final velocity, acceleration, and time. The specific equation we need is: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.

Since the boat comes to a complete stop before the engine is engaged again, its final velocity v is 0 m/s. Its initial velocity u is given as 2.2 m/s, and the displacement s is 10 m. Substituting these values into the equation and solving for acceleration a gives: a = −(u^2) / (2s).

Once the acceleration is known, we can use the equation v = u + at to find the time t, knowing that v is 0 m/s at the end of the coasting period.