The powerboat, starting from rest, maintains a constant acceleration. After a certain time t, its displacement and velocity are r and v. At time 2t, what would be its displacement and velocity, assuming the acceleration remains the same?Question 2Answeri.4r and 4vii.2r and 4viii.4r and 2viv.2r and 2v
Question
The powerboat, starting from rest, maintains a constant acceleration. After a certain time t, its displacement and velocity are r and v. At time 2t, what would be its displacement and velocity, assuming the acceleration remains the same?Question 2Answeri.4r and 4vii.2r and 4viii.4r and 2viv.2r and 2v
Solution
The displacement (r) and velocity (v) of an object under constant acceleration can be described by the equations of motion:
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r = ut + 0.5at^2, where u is the initial velocity, a is the acceleration, and t is the time. Since the powerboat starts from rest, u = 0, so r = 0.5at^2.
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v = u + at. Again, since the powerboat starts from rest, u = 0, so v = at.
At time 2t:
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The displacement would be r' = 0.5a(2t)^2 = 2at^2 = 4 * 0.5at^2 = 4r.
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The velocity would be v' = a(2t) = 2at = 2v.
So, the correct answer is i. 4r and 2v.
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