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

The distance traveled by the boat can be calculated using the kinematic equation:

Distance = Initial velocity x time + 1/2 x acceleration x time^2
Given:
– Initial velocity (u) = 0 m/s (starting from rest)
– Acceleration (a) = 3.0 m/s²
– Time (t) = 8.0 s

Using the kinematic equation:
Distance} = 0 x 8 + 1/2 x 3.0 x 8^2
Distance = 0 + 1/2 x 3.0 x 64
Distance = 1/2 x 192
Distance = 96

Therefore, the boat travels a distance of 96 meters during the 8.0 seconds of constant acceleration.