Question

A hundred meter sprinter increases her speed from rest uniformly at the rate of 1.5m/s2 up to three quarters of the total run and covers the last quarter with uniform speed. How much time does she take to cover the first half and the second half of the run? pls no links.....

Answer 1

The calculation is as follows:

Use equation of motions: SUVAT
s-displacement, u-initial velocity, v-final velocity,a- acceleration, t-time

v=u + atv2 = u2 + 2ass=1/2(u+v)ts=ut + 1/2at2
The first part AB:  u= 0m/s
                             a= 1.5m/s2
                             s= 75m
                             
therefore time taken s= ut + 1/2at2
                                 75=1/2 x 1.5 x t2
                                 t2= 150/1.5
                                 t2= 100
                                t=  10s
Therefore time taken in the first part is 10 seconds

Time taken in part 2 BC:

final velocity (v)= 0m/s
displacement (s)= 25m

Initial velocity (u) will be given by the final velocity of the first part:

u-0   s-75   a-1.5m/s2

v2=u2+2as
 v2=2x1.5x75
 v2= 225
 therefore v = 15m/s (this would be the initial velocity for the second                                           part)                             

time will be given by:

s=1/2(u+v)t
25=1/2(0+15)t
25=15/2t

t= 25x2/15     t =3.333seconds
Time taken in the last part is 3.333 seconds