Question

A bugler has a start with an acceleration of 2m/s^2 a police vigilante came after 5seconds and countitune to chase the bugler's car with a uniform velocity of 20m/s. Find the time taken for the police van will over take the bugler's car

Answer 1

Let t is time taken by burglar's car before catching the police .

in case of burglar ,
initial velocity, u = 0
acceleration, a = 2 m/s²

distance covered in t sec , S = ut + 1/2at²
S = 0 + 1/2 × 2 × t² = t² .........(1)

in case of police,
uniform velocity, v = 20 m/s
a/c to question, police approach the burglar's car after 5 second.
so, distance covered in (t - 5)sec , S = 20(t - 5)......(2)

if police van overtakes the burglar's car.
t² = 20(t -5)
t² - 20t + 100 = 0
t² - 2 × 10t + (10)² =0
(t - 10)² = 0
t = 10 sec .

hence, time taken for the police van will overtake the burglar's car = 10 -5 =5 sec.