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?
Solution and Explanation
Given Initial velocity of motorboat, \(u\) = \(0\)
Acceleration of motorboat, \(a\) = \(3.0\) \(m s^{-2}\)
Time under consideration, \(t\) = \(8.0\) \(s\)
We know that Distance, \(s\) = \(ut\) + \(\bigg(\frac{1}{2}\bigg)at^2\)
Therefore, The distance travel by motorboat = \(0 \times 8 + \bigg(\frac{1}{2}\bigg)3.0 \times 8 ^2\)
= \(\bigg(\frac{1}{2}\bigg) \times 3 \times 8 \times 8\) m
= \(96\) \(m\)
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In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration.
