A bullet when fired into a target loses half of its velocity afte

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 Multiple Choice QuestionsMultiple Choice Questions

21.

A particle starting with certain initial velocity and uniform acceleration covers a distance of 12 m in first 3 s and a distance of 30 m in next 3 s. The initial velocity of the particle is

  • 3 ms-1

  • 2.5 ms-1

  • 1 ms-1

  • 1.5 ms-1


22.

The coordinates of a particle moving in x-y plane at any instant of time t are x = 4t2 ; y = 3t2. The speed of the particle at that instant is

  • 10t

  • 5t

  • 3t

  • 2t


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23.

A bullet when fired into a target loses half of its velocity after penetrating 20 cm. Further distance of penetration before it comes to rest is

  • 6.66 cm

  • 3.33 cm

  • 12.5 cm

  • 10 cm


A.

6.66 cm

Given, Initial velocity, U = v

Final velocity, V = v2

Distance, s = 20 cm

Let, the further distance of penetration before it comes to rest be x.

             V2 = U2 - 2as  v22 = v2 - 2a × 20   40 a = v2 - v24   40 a = 3 v24                    ......... (i)and v2 = u2 + 2as       v2 = 0 + 2a × 20 + x       v2 = 2 × 3160 v2 × 20 + x        From Eq.(i)        1 = 380 20 + x     803 = 20 + x         x = 803 - 20         x = 80 - 603 = 203         x = 6.66 cm


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24.

The distance x covered by a particle varies with time t as x2 = 2t2 + 6t + 1. Its acceleration varies with x as

  • x

  • x2

  • x-1

  • x-3


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25.

A particle moving along a straight line covers half of the distance with a speed of 3 ms-1. The other half of the distance is covered in two equal time intervals with speed of 4.5 ms-1 and 7.5 ms-1. The average speed of the particle (in ms-1) is

  • 5.0

  • 5.5

  • 5.8

  • 4.0


26.

Two cars started moving with initial velocities v and 2 v. For the same deceleration, their respective stopping distances are in the ratio

  • 1 : 1

  • 1 : 2

  • 1 : 4

  • 2 : 1


27.

The distances traversed during equal intervals of time by a freely falling body from rest are in the ratio

  • 1 : 3 : 5 : 7 ....

  • 2 : 4 : 6 : 8 .....

  • 1 : 4 : 9 : 25 .....

  • 1 : 9 : 25 : 49 .....


28.

A ball is hung by a string from the ceiling of a car moving on a straight and smooth road. If the string is inclined towards the front side of the car making a small constant angle with the vertical, then the car is moving with

  • constant velocity

  • constant acceleration

  • constant retardation

  • increasing acceleration


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29.

A girl in a swing is 2.5 m above ground at the maximum height and at 1.5 m above the ground at the lowest point. Her maximum velocity in the swing is (g = 10 ms-2)

  • 52 ms-1

  • 25 ms-1

  • 23 ms-1

  • 32 ms-1


30.

A car moves a distance of 200 m. It covers first half of the distance at speed 60 kmh-1 and the second half at speed v. If the average speed is 40 kmh-1, the value of v is

  • 30 kmh-1

  • 13 kmh-1

  • 60 kmh-1

  • 40 kmh-1


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