Question

A 100 m sprinter increases her speed from rest uniformly at the rate of 1 m/s² upto 40 m and covers the remaining distance with a uniform speed. The sprinter covers the first half of the run in t₁s and second half in t₂s, then 

A. t₁ > t₂ 

B. t₁ < t₂ 

C. t₁ = t₂ 

D. information given is incomplete

Answer 1

For the first 40 m: 

Using the third equation of motion: v² – u² = 2] 

as 

where: 

s = distance covered = 40 m 

v = final velocity = ? m/s 

u = initial velocity = 0 m/s 

a = acceleration = 1 m/s² 

v² – u² = 2 

as 

v² – 0 = 2 × 1 × 40 

v² = 80 

v = 8.94 m/s 

Using the first equation of motion: v = u + at 

where:

v = final velocity = 8.94 m/s 

u = initial velocity = 0 m/s 

a = acceleration = 1 m/s² 

t₁ = time = ?s 

v = u + at₁ 

8.94 = 0 + 1 × t₁ 

t₁ = 8.94s 

Here its given the speed is uniform not velocity, therefore 

acceleration will be 1 m/s² and speed will be 8.94 m/s everywhere. 

Using the third equation of motion: v² – u² = 2 

as 

where: 

s = distance covered = 60 m 

v = final velocity = ?? m/s 

u = initial velocity = 8.94 m/s 

a = acceleration = 1 m/s² 

v² – u² = 2 

as 

v² – (8.94)² = 2 × 1 × 60 

v² - 80 = 120 

v² = 120 + 80 = 200 

v = 14.14 m/s 

Using the first equation of motion: v = u + at 

where: 

v = final velocity = 14.14 m/s 

u = initial velocity = 8.94 m/s 

a = acceleration = 1 m/s² 

t₂ = time = ?s 

v = u + at₂ 

14.14 = 8.94 + 1 × t₂ 

t₂ = 14.14 – 8.94 

t² = 5.2 secs