Question:

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 ms^-2 for 8.0 s. How far does the boat travel during this time ?

Solution: Distance traveled

Initial velocity of the motorboat (u) =0 (since the boat starts from rest)

Acceleration (a) =3 ms^-2

Time taken (t) = 8 s

How far the boat travel is the distance (s)

Second equation of motion:

The second equation of motion is $${s=ut+\frac{1}{2}at^2}$$

We can substitute the above values

Distance traveled:

$${s=0(8)+\frac{1}{2} (3) (8)^2}$$

$${s= 0 +\frac{1}{2} (3) (8)(8)}$$

$${s=96 m}$$

Hence the boat travels 96 m.

Conclusion:

Boat travels during the time 8 s with a constant rate 3.0 ms^-2 is 96 m