Question

a burgulars cars ahead and start with an acceleration of 2 metre per second square a police vigilant party came after 5 seconds and continued to chase the burglars cars with a uniform velocity of 20 metre per second. find the time in which the police van overtakes the burglars car.

Answer 1

Burgular's Car (Given)
Initial velocity = 0 m/s
acceleration = 2 m/s²

Police Vigilant Party (Given)
Velocity = 20 m/s

Now,
If the police comes after 5 seconds,
then,
Distance covered by burgular's Car in 5 seconds will be,

$s = ut + \frac{1}{2} a {t}^{2} \\ s = 0 \times t + \frac{1}{2} \times 2 \times {5}^{2} \\ s = 0 + 25\\ s = 25 \: metres$
Now,

Let the time taken to over take the burgular's Car be x

then,

Distance covered by police = Distance covered by the Burgular's Car + 25.

(v × t) = $(ut + \frac{1}{2} a {t}^{2} ) + 25$

(20 * x) = $(10 \times x + \frac{1}{2} \times 2 \times {x}^{2} ) + 25$

20x = x² +10x + 25
0 = x² + 10x - 20x + 25
0 = x² - 10x + 25
0 = x² - 5x - 5x +25
0 = x(x-5) -5(x-5)
0 = (x-5) (x-5)

x = 5 seconds.

After 5 seconds the police car will overtake the Burgular's Car.

Answer 2

Given the solution

Hope it helps