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
Answers
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