Assuming that the ball does not hit the floor within the first second of motion, which of these graphs represents the speed of the ball plotted against time?

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Answer 1 · 2018-04-16T00:38:06

D

Since the acceleration #g# is given by #0.4 t " ms"^-2#, we have

#(dv)/dt = g(t) implies dv = g(t)dt = alpha t dt#

where #alpha = 0.4# (in SI units).

We know #v(0) = 0#

So

#v(t)-v(0) = int_0^t g(t^')dt^'=int_0^t alpha t^'dt^' = 1/2 alpha t^2#

or

#v(t) = 0.2 t^2#

Thus the speed-time graph should be a parabola going through #(0,0)# and #(1,0.2)#.