Question

A 100 m splinter uniformly increases his speed from rest at the rate if 1m/s.find final speed

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