Question

A sprinter accelerates uniformly to his top speed after running 30 metres of a 100 metre race. He maintains this speed for the reminder of the race and takes 10.4 seconds to complete it. Find:

a) the top speed of the athlete
b) the time taken to reach the top speed

Answer 1

b) 4.8 seconds..

Answer 2

top speed is 12.5 metres/second..

Answer 3

do i have to explain?

Answer 4

yes please

Answer 5

i got the same answer

Answer 6

i got this by visualizing the problem as a graph of velocity over time...

Answer 7

so there's a plot of velocity over time. uniform acceleration until a time I'm calling T30 (the time at which he reached 30 meters), at a velocity of Vmax.

You know since this is a V-T curve, the area under the curve is the distance travelled. And you know the equation for area in a triangle is 1/2 b*h, and a rectangle is just l*w. knowing all this I set up 2 equations:

0.5 * T30 * Vmax = 30 (the area of the initial triangle is 30)
(10.4-T30)*Vmax = 70 (the remaining time he ran the race at a constant speed of vmax, he covered 70 meters, since the race was 100 meters total)

Solve those two equations simultaneously and you get T30 = 4.8 Vmax = 12.5.