Question

A motorboat starting from a dead stop accelerates at a constant 1.7 m/s² for 2.5 s, then very rapidly roars up to 4.4 m/s² and holds it constant for 4.0 s. What is its average acceleration over the first 4.9 s of motion? 

 

What is its speed after 6.5 s? 

Next the boat decelerates to a stop in 19.0 s at a constant rate. What is the boat's acceleration during this last portion of the trip? 

 

Answer 1

$<a>=\frac{v}{t_{4.9}}=\frac{a_{1.7}t_{2.5}+a_{4.4}t_{4.9-2.5}}{t_{4.9}}=3.0~\frac{\text{m}}{\text{s}^2},$

$v_{6.5}={a_{1.7}t_{2.5}+a_{4.4}t_{4.0}}=21.85~\frac{\text{m}}{\text{s}},$

$a=\frac{v_{6.5}}{t_{19}}=1.15~\frac{\text{m}}{\text{s}^2}.$