Question

Physics :-

Robbers in a car travelling at 20m/s pass a policeman on a motorcycle at rest. The policeman immediately starts chasing the Robbers. The policeman accelerates at 3m/s square for 12s and thereafter travels at a constant velocity. Calculate the distance covered by the policeman before he overtakes the car.

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Answer 1

Answer:

Explanation:

The distance covered by the policeman in 12 sec

s = ut + 1/2 at2

= 0 x12 + 0.5 x3 x 12x12 = 216m

v = u + at = 0 + 12x3 = 36m/s

The distance covered by the robber in 12 sec

s = 20 x 12 = 240m

Suppose he over takes in 12 + t sec, in which he travels = 216 + 36 * t

r robbers will travel in the same time 20 * ( 12+t) m

216 + 36 t = 240 + 20 t

t = 24 / 16 = 1.5 s

Distance travelled by policeman in 12 + 1.5 = 13.5 s

= 216 + 36 x 1.5 = 270 m

Answer 2

Solution :-

As given

▪️Velocity of Robbers car = 20 m/s

▪️Intial Velocity of Police man's bike = 0

▪️Acceleration of Police man's bike = 3 m/s²

▪️Time for acceleration = 12 sec

Now first of all we will check what will be the distance covered by Police man's bike in first 12 sec .

For Police man's bike :-

S = ut + 1/2 at²

S = 0(12) + 1/2 (3) × 12²

S = 0 + 1/2 × 3 × 144

S = 216 m

For Robbers car

S = ut

S = 20 × 12

S = 240 m

So we can see in the period of constant Acceleration the bike was unable to overtake the bike.

Now the bike will travel with a uniform speed

v = u + at

→ v = 0 + 3(12)

→ v = 36 m/s

Now difference in distance covered in 12 sec

= 240 - 216

= 24 m

Now let the time be "t" in which the bike have to cover x + 24 m and The Car have to cover x m distance :-

For bike :-

→ x + 24 = 36t ...(i)

For car :-

→ x = 20t ..(ii)

Now by subtracting (ii) from (i)

x + 24 = 36t

- x = 20t

______________

24 = 16t

$\rightarrow t = \dfrac{24}{16}$

$\rightarrow t = \dfrac{3}{2}$

$\rightarrow t = 1.5 \: sec$

Now we have got the time , So as the police man's bike was in constant motion in this period .

Hence ,distance travelled during this period

= 36 × 1.5

= 54 m

Now total distance

= Distance travelled during Acceleration period + Distance travelled during constant motion period.

= 216 + 54

= 270 m