Motion in Straight Line

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

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

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

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

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

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 .....

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

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)

• $5\sqrt{2} {\mathrm{ms}}^{-1}$

• $2\sqrt{5} {\mathrm{ms}}^{-1}$

• $2\sqrt{3} {\mathrm{ms}}^{-1}$

• $3\sqrt{2} {\mathrm{ms}}^{-1}$

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

A bus begins to move with an acceleration of 1 ms^-2. A man who is 48 m behind the bus starts running at 10 ms^-1 to catch the bus. The man will be able to catch the bus after 

• 6 s

• 5 s

• 8 s

• 7 s