1.

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»

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


Discussion

No Comment Found

Related InterviewSolutions