A sprinter has to cover a total run of 100 m. She increases her speed from rest under a uniform acceleration of 1.0 m/s2 up to three quarters of the total run and covers the last quarter him uniform speed. The time she takes to cover the first half, and to cover the second half of the run will be
Using the second equation of motion: s = ut + 
at2
where: s = distance covered = 75 m
u = initial velocity = 0 m/s
a = acceleration = 1 m/s2
t = time = ts
s = ut + 
at2
75 = 0 + 
× 1 × t2
75 × 2 = t2
150 = t2
t = 12.24 s
Using the third equation of motion: v2 – u2 = 2as
where: s = distance covered = 75 m
v = final velocity = ?? m/s
u = initial velocity = 0 m/s
a = acceleration = 1 m/s2
v2 – u2 = 2as
v2 = 2 × 1 × 75 = 150
v = 12.24 m/s
For second part distance is 25 m.
Using the second equation of motion: s = ut + 
at2
where: s = distance covered = 25 m
u = initial velocity = 12.24 m/s
a = acceleration = 1 m/s2
t = time = ts
s = ut + 
at2
25 = 12.24t + 
1 x t2
t2 + 24.48t – 50 = 0
t = 1.99 s