Question

A boat is cruising in a straight line at a constant speed of 2.6 m/s when it is shifted into a neutral. After coasting 12m the engine is engaged again, and the boat resumes cruising at the reduced constant speed of 1.6 m/s. Assuming constant acceleration while coasting. How long did it take for the boat to coast the 12m? What was the boat's acceleration while it was coasting? When the boat had coasted for 6.0 m,was its speed 2.1m/s, more than 2.1m/s,or less than 2.1m/s ? Explain.

Answer 1

Answer:

time = 5.71 s

acceleration = -0.175 m/s²

v = 2.16  m/s

It is more than 2.1 m/s

Explanation:

given data

constant speed u = 2.6 m/s

distance s = 12 m

reduced constant speed v = 1.6 m/s

solution

we find how long it takes for the boat to coast the 12 meters

time = $\frac{d}{0.5*(v+u)}$

time = $\frac{12}{0.5*(1.6+2.6)}$

time = 5.71 s

we will apply equation of motion for During its coasting  that is

v² - u² = 2as    .........................1

here u is initial velocity i.e. 2.6 m/s and v is final velocity i.e 1.6 m/s and s is distance

1.6² - 2.6² = 2×a×12

a= -0.175 m/s²

and

When it coast 6 m then from equation 1  

v² - u² = 2as

v² - 2.6² = 2×(-0.175)×12

v = 2.16  m/s

It is more than 2.1 m/s