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?

Question

704 views around the world

You can reuse this answer
Creative Commons License

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)#.