Motion in a Straight Line

When a ruler falls vertically, 5 different persons catch it with different reaction times. (g = 9.8 ms-2) What is the correct order of the distance travelled by the ruler for each person ?

1. B > E > A > C > D
2. C > D > A > E > B
3. C > D > A > B > E
4. B > E > A > D > C

The following plots show variation of velocity (v) with time (t), of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct? [figure]

1. B only
2. A and E only
3. C only
4. D only

Consider a particle moving along a straight line, whose position as a function of time is given by s(t) = t2 - t + , where = 1 m s-2, = 6 m s-1 and = 5 m. The average speed of the particle, in m s-1 from t = 0 to t = 6 s is:

1. 0
2. 12
3. 6
4. 3

In some appropriate units, time (t) and position (x) relation of a moving particle is given by t = x2 + x. The acceleration of the particle is

1. + 2(x+1)3
2. + 22x+1
3. - 2(x+2)3
4. - 2(2x+1)3

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

1. 10 min, 90 km/h
2. 15 min, 120 km/h
3. 9 min, 40 km/h
4. 25 min, 100 km/h

The velocity (v)- time (t) plot of the motion of a body is shown below: [figure] The acceleration (a)- time (t) graph that best suits this motion is :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A particle is moving along x-axis with its position (x) varying with time (t) as x = t4 + t2 + t + . The ratio of its initial velocity to its initial acceleration, respectively, is:

1. 2 :
2. : 2
3. 4 :
4. : 2

A vehicle travels half the distance with speed v and the remaining distance with speed 2v. Its average speed is :

1. 2v3
2. 4v3
3. 3v4
4. v3

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity 4 m s-1. The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take g = 10 m s-2)

1. 60 m
2. 64 m
3. 68 m
4. 56 m

A bullet from a gun is fired on a rectangular wooden block with velocity u. When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes u3. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

1. 24 cm
2. 28 cm
3. 30 cm
4. 27 cm

The ratio of the distances travelled by a freely falling body in the 1st, 2nd, 3rd and 4th second

1. 1 : 2 : 3 : 4
2. 1 : 4 : 9 : 16
3. 1 : 3 : 5 : 7
4. 1 : 1 : 1 : 1

The displacement-time graphs of two moving particles make angles of 30 and 45 with the x-axis as shown in the figure. The ratio of their respective velocity is [figure]

1. 3 : 1
2. 1 : 1
3. 1 : 2
4. 1 : 3

The position-time (x - t) graph for positive acceleration is

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let Sn be the distance travelled by the block in the interval t = n - 1 to t = n. Then the ratio SnSn+1 is :

1. 2n2n-1
2. 2n-12n
3. 2n-12n+1
4. 2n+12n-1

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s2)

1. 340 m
2. 320 m
3. 300 m
4. 360 m

When an object is shot from the bottom of a long smooth inclined plane kept at an angle 60 with horizontal, it can travel a distance x1 along the plane. But when the inclination is decreased to 30 and the same object is shot with the same velocity, it can travel x2 distance. Then x1 : x2 will be :

1. 1 : 2
2. 2 : 1
3. 1 : 3
4. 1 : 2 3

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E. Due to the force q E, its velocity increases from 0 to 6 m s-1 in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

1. 2 m s-1, 4 m s-1
2. 1 m s-1, 3 m s-1
3. 1 m s-1, 3.5 m s-1
4. 1.5 m s-1, 3 m s-1

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t1. On another day, if she remains stationary on the moving escalator, then the escalator takes her up in time t2. The time taken by her to walk up on the moving escalator will be

1. t1t2t2-t1
2. t1t2t2+t1
3. t1-t2
4. t1+t22

If the velocity of a particle is v = At + Bt2, where A and B are constants, then the distance travelled by it between 1 s and 2 s is

1. 32A + 73B
2. A2 + B3
3. 32A + 4B
4. 3A + 7B

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by xP(t) = (at + bt2) and xQ(t) = (ft - t2). At what time do the cars have the same velocity ?

1. a-f1+b
2. a+f2(b-1)
3. a+f2(1+b)
4. f-a2(1+b)

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to v(x) = x-2n, where and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by

1. -2 2x-2n+1
2. -2n 2e-4n+1
3. -2n 2x-2n-1
4. -2n 2x-4n-1

A stone falls freely under gravity. It covers distances h1, h2 and h3 in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relation between h1, h2 and h3 is

1. h2 = 3h1 and h3 = 3h2
2. h1 = h2 = h3
3. h1 = 2h2 = 3h3
4. h1 = h23 = h35

The displacement 'x' (in meter) of a particle of mass 'm' (in kg) moving in one dimension under the action of a force, is related to time 't' (in sec) by t = x + 3. The displacement of the particle when its velocity is zero, will be

1. 4 m
2. 0 m (zero)
3. 6 m
4. 2 m

A stone is dropped from a height h. It hits the ground with a certain momentum P. If the same stone is dropped from a height 100% more than the previous height, the momentum when it hits the ground will change by

1. 68%
2. 41%
3. 200%
4. 100%

The motion of a particle along a straight line is described by equation x = 8 + 12t - t3 where x is in metre and t in second. The retardation of the particle when its velocity becomes zero is

1. 24 m s-2
2. zero
3. 6 m s-2
4. 12 m s-2

A particle covers half of its total distance with speed v1 and the rest half distance with speed v2. Its average speed during the complete journey is

1. v1+v22
2. v1v2v1+v2
3. 2v1v2v1+v2
4. v12v22v12+v22

A boy standing at the top of a tower of 20 m height drops a stone. Assuming g = 10 m s-2, the velocity with which it hits the ground is

1. 10.0 m/s
2. 20.0 m/s
3. 40.0 m/s
4. 5.0 m/s

A particle moves a distance x in time t according to equation x = (t + 5)-1. The acceleration of particle is proportional to

1. (velocity)3/2
2. (distance)2
3. (distance)-2
4. (velocity)2/3

A ball is dropped from a high rise platform at t = 0 starting from rest. After 6 seconds another ball is thrown downwards from the same platform with a speed v. The two balls meet at t = 18 s. What is the value of v? (Take g = 10 m/s2)

1. 75 m/s
2. 55 m/s
3. 40 m/s
4. 60 m/s

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then

1. S2 = 3S1
2. S2 = 4S1
3. S2 = S1
4. S2 = 2S1