Question

A big boat and a small boat are moving at the same speed and begin slowing down to a stop. The big boat takes less time to stop. Which boat has a greater average acceleration (magnitude) during this stop?

• A. The big boat
• B. The small boat
• C. The boats have the same average acceleration
• D. The boat's relative accelerations cannot be determined
• E. The boats are not accelerating

Answer 1

Answer: (A)

The big boat

Let u be the initial velocity of both the boats , as both boats stop at last therefore their final velocity v will be zero .

now by $v=u-at$ , a is taken negative because boats are slowing down so it is deceleration ,

for big boat $v=u-a_1{t}_1$

or $a_1=(u-v)/t_1=u/t_1$ , as $v=0$ ,

where $t_1=$ time taken by big boat to stop ,

similarly ,

for small boat $a_2=u/t_2$

now given that $t_1<t_2$ therefore $a_1>a_2$ .

a1>a2acceleration of the big boat is larger than small one .