A motor boat starting from rest on a lake accelerate in a straight line at a constant rate of 3m/s for 8s. How far does the boat travel during the time?

d=1/2 a t^2

To find the distance the boat travels during the 8-second time period, we can use the formula:

Distance = Initial Velocity * Time + (1/2) * Acceleration * Time^2

Since the boat starts from rest, its initial velocity is 0 m/s. The acceleration is given as 3 m/s^2, and the time is 8 seconds.

Plugging these values into the formula, we have:

Distance = 0 * 8 + (1/2) * 3 * (8^2)
Distance = 0 + (1/2) * 3 * 64
Distance = 0 + (1/2) * 3 * 64
Distance = 0 + (1/2) * 3 * 64
Distance = 0 + (1/2) * 3 * 64
Distance = 0 + 1.5 * 64
Distance = 0 + 96
Distance = 96 meters

Therefore, the boat travels a distance of 96 meters during the 8-second time period.