Question

A 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 will be its displacement and velocity, assuming the acceleration remains constant?

a) 2r and 2v
b) 2r and 4v
c) 4r and 2v
d) 4r and 4v

Answer 1

Answer: Ok, so you know the acceleration, lets call it A.

now, the velocity will take the form of V= A*t + v0, where v0 is the inicial velocity, in this case the boat starts from the rest, so v0 = 0

integrating again you obtain R = (A*t*t)/2 + r0, and we will take r0 = 0.

so, at a time t₁ we have a velocity V = v = A*t₁

R = r = (A*t₁*t₁)/2

so a t₂=2*t₁

V= A*2*t₁= 2v

R= 0.5*A*t₁*t₁*4 = 4r

so the answer is c.