Motion in a Straight Line

A gas balloon is going up with a constant velocity of 10 m/s. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is m. (Take g=10 m/s2)

1. 85
2. 150
3. 129
4. 125

The velocity (v) versus time (t) plot of a particle is shown in the figure, for a time interval of 40 s. The total distance travelled by the particle and the average velocity during this period are, respectively . [figure]

1. 25 m and zero
2. 50 m and zero
3. 100 m and zero
4. 100 m and 2.5 m/s

Two cars A and B are moving in the same direction along a straight line with speeds 100 km/h and 80 km/h, respectively such that car A is moving ahead of car B. A person in car B throws a stone with a speed v so that it hits the car A with a speed of 5 m/s. The value of v is km/h.

1. 18
2. 28
3. 38
4. 48

A particle of mass m falls from rest through a resistive medium having resistive force, F = -kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t) ?

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

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is m. (g = 10 m/s2)

1. 3.8
2. 4.0
3. 4.2
4. 2.5

A particle starts moving from time t = 0 and its coordinate is given as x(t) = 4t3 - 3t Choose the correct answer from the options given below :

1. A, C, D Only
2. A, B, C Only
3. C, E Only
4. A, C Only

The velocity (v) – distance (x) graph is shown in figure. Which graph represents acceleration (a) versus distance (x) variation of this system? [figure]

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

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with 3 m/s2. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is 5 m/s. The initial height of the airplane is m. (g = 10 m/s2)

1. 92.5
2. 62.5
3. 20
4. 82.5

The displacement x versus time graph is shown below. [figure] Choose the correct answer from the options given below :

1. (B), (C), (D) only
2. (B), (D), (E) only
3. (A), (D), (E) only
4. (B), (C), (E) only

Which of the following curves possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below :

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

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x = c0 (t2 - 2 ) + c(t - 2)2 where c0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

1. the acceleration of the particle is 2(c + c0)
2. the acceleration of the particle is 2c0
3. the acceleration of the particle is 2c
4. the initial velocity of the particle is 4c

A sportsman runs around a circular track of radius r such that he traverses the path ABAB. The distance travelled and displacement, respectively, are [figure]

1. r, 3r
2. 2r, 3 r
3. 3 r, 2r
4. 3 r, r

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between t = 0 to t = 4 s? [figure]

1. 11 m
2. 30 m
3. 13 m
4. 10 m

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is km . [figure]

1. 12
2. 6
3. 3
4. 9

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is :

1. 9.2 m/s
2. 8.8 m/s
3. 10 m/s
4. 8 m/s

Two cars are travelling towards each other at speed of 20 m s-1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of 2 m s-2. The distance between them when they come to rest is :

1. 25 m
2. 100 m
3. 50 m
4. 200 m

A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed for time 3t. The average speed of the train for this duration of journey will be (in km/h) :

1. 70
2. 40
3. 30
4. 80

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in t1. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in t2. Time required to reach the ground, if it is dropped from the top of the tower, is :

1. t1 + t2
2. t1 t2
3. t1t2
4. t1 - t2

A body travels 102.5 m in nth second and 115.0 m in (n+2)th second. The acceleration is :

1. 6.25 m/s2
2. 5 m/s2
3. 12.5 m/s2
4. 9 m/s2

A cyclist starts from the point P of a circular ground of radius 2 km and travels along its circumference to the point S. The displacement of a cyclist is: [figure]

1. 8 km
2. 4 km
3. 6 km
4. 8 km

Train A is moving along two parallel rail tracks towards north with speed 72 km/h and train B is moving towards south with speed 108 km/h. Velocity of train B with respect to A and velocity of ground with respect to B are (in ms-1):

1. -50 and -30
2. -50 and 30
3. -30 and 50
4. 50 and -30

The relation between time 't' and distance 'x' is t= x2+ x, where and are constants. The relation between acceleration (a) and velocity (v) is :

1. a=-5 v5
2. a=-3 v2
3. a=-2 v3
4. a=-4 v4

A body starts moving from rest with constant acceleration covers displacement S1 in first (p-1) seconds and S2 in first p seconds. The displacement S1+S2 will be made in time :

1. (2p+1) s
2. (2p-1) s
3. (2p2-2p+1 )s
4. (2p2-2p+1 ) s

A particle is moving in a straight line. The variation of position 'x' as a function of time 't' is given as x= (t3-6t2+20t+15 )m. The velocity of the body when its acceleration becomes zero is :

1. 6 m/s
2. 10 m/s
3. 8 m/s
4. 4 m/s

A bullet is fired into a fixed target loses one third of its velocity after travelling 4 cm. It penetrates further D 10-3 m before coming to rest. The value of D is :

1. 2
2. 5
3. 3
4. 4