Question

A thief Run with a uniform speed of hundred metre per minute after 1 minute a policeman runs after the thief to catch him goes with a speed of 100 M per minute in the first minute and increases speed by 10 M per minute every succeeding minute after how many minutes the policeman will catch the thief

Answer 1

Answer:

t=1.43 minutes

Step-by-step explanation:

Thief's initial velocity is u1 = 100m/min = 100m/60sec = 5/3 m/s

Police initial velocity is u2 = 100m/min = 5/3 m/s

As police speed is increasing every minute i.e.

Acceleration of police is 10m/min = 1/6 m/sec^2

As thief ran for 1 minute that means have to calculate his displacement in 1 minute so

u1=5/3 m/s          as accelerations of thief is zero(constant velocity)

velocity = displacement/time

5/3=disp./60sec

disp.=5*60 / 3

disp.=100 metre

so the police ran in constant velocity after the thief for 1 minute i.e. the distance between them will remain same

so the real questions starts after 1 minute = 60 seconds

s= 100m

u2=5/3 m/sec

a2=1/6 m/sec^2

so s=ut + 1/2at^2

put values

100 = 5/3t + 1/12t^2

so calculate t by quadratic equation

t=26 seconds

we will add 60 seconds as he ran for 100 metre with same speed without accelerating

t=26+60=86 seconds

t=1.43(approx) minutes