Motion in a Straight Line (Uniformly Accelerated Motion & Relative Motion)Contact Number: 8527521718Motion in a Straight Line (Uniformly Accelerated Motion & Relative Motion)Contact Number: 8527521718A car \(A\) is traveling on a straight level road at a uniform speed of \(60\) km/h. It is followed by another car \(B\) which is moving at a speed of \(70\) km/h. When the distance between them is \(2.5\) km, car \(B\) is given a deceleration of \(20\) km/h2. After how much time will car \(B\) catch up with car \(A\)?
1. \(1\) hr
2. \(\frac{1}{2}\) hr
3. \(\frac{1}{4}\) hr
4. \(\frac{1}{8}\) hr
A jet airplane travelling at the speed of \(500~\text{km/h}\) ejects its products of combustion at the speed of \(1500~\text{km/h}\) relative to the jet plane. What is the speed of the latter with respect to an observer on the ground?
1. \(1000~\text{km/h}\)
2. \(500~\text{km/h}\)
3. \(1500~\text{km/h}\)
4. \(2000~\text{km/h}\)
A car travelling at a speed of \(30\) km/h is brought to rest at a distance of \(8\) m by applying brakes. If the same car is moving at a speed of \(60\) km/h, then it can be brought to rest with the same brakes in:
1. \(64\) m
2. \(32\) m
3. \(16\) m
4. \(4\) m
A balloon starts from the ground from rest with an upward acceleration of \(2\) m/s2. After \(1\) sec, a stone is dropped from it. The time taken by the stone to strike the ground is approximately:
| 1. | \(0.3\) s | 2. | \(0.7\) s |
| 3. | \(1\) s | 4. | \(1.4\) s |
Two balls are projected upward simultaneously with speeds of \(40\) m/s and \(60\) m/s. The relative position \((x)\) of the second ball with respect to the first ball at time \(t=5\) s will be: (neglect air resistance)
1. \(20\) m
2. \(80\) m
3. \(100\) m
4. \(120\) m
A body is thrown vertically up from the ground. It reaches a maximum height of \(100\) m in \(5\) s. After what time will it reach the ground from the position of maximum height?
| 1. | \(1.2\) s | 2. | \(5\) s |
| 3. | \(10\) s | 4. | \(25\) s |
A ball is thrown vertically upwards from the top of a tower at . It strikes the pond near the base of the tower after 3 seconds. The height of the tower is:
1. 73.5 m
2. 44.1 m
3. 29.4 m
4. None of these
A particle when thrown moves such that it passes from the same height at 2 sec and 10 sec, the height is:
1. g
2. 2g
3. 5g
4. 10g
Four marbles are dropped from the top of a tower one after the other at a one-second interval. The first one reaches the ground after \(4\) seconds. When the first one reaches the ground the distances between the first and second, the second and third, and the third and fourth will be, respectively:
| 1. | \(35\) m, \(25\) m, and \(15\) m | 2. | \(30\) m, \(20\) m, and \(10\) m |
| 3. | \(20\) m, \(10\) m, and \(5\) m | 4. | \(40\) m, \(30\) m, and \(20\) m |
A body is thrown upwards and reaches its maximum height. At that position:
| 1. | its velocity is zero and its acceleration is also zero. |
| 2. | its velocity is zero but its acceleration is maximum. |
| 3. | its acceleration is minimum. |
| 4. | its velocity is zero and its acceleration is the acceleration due to gravity. |
The effective acceleration of a body, when thrown upwards with acceleration a will be:
1.
2.
3.
4.
If a body is thrown up with the velocity of \(15\) m/s, then the maximum height attained by the body is: (assume \(g = 10\) m/s2)
1. \(11.25\) m
2. \(16.2\) m
3. \(24.5\) m
4. \(7.62\) m
The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane \(9.8~\text{m}\) long (angle of inclination is \(30^{\circ}\)
| 1. | \(\frac{1}{2}~\text{sec} \) | 2. | \(2 ~\text{sec} \) |
| 3. | \(4~ \text{sec} \) | 4. | \(1~\text{sec} \) |
If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three seconds, the time of the travel is:
1. \(6\) sec
2. \(5\) sec
3. \(4\) sec
4. \(3\) sec
A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds?
1. h/9 meters from the ground
2. 7h/9 meters from the ground
3. 8h/9 meters from the ground
4. 17h/18 meters from the ground
| 1. | \(t_1<t_2 \) or \(t_1>t_2 \) depending upon whether the lift is going up or down. |
| 2. | \(t_1<t_2 \) |
| 3. | \(t_1>t_2 \) |
| 4. | \(t_1=t_2 \) |
A student is standing at a distance of \(50\) metres from the bus. As soon as the bus begins its motion with an acceleration of \(1\) ms–2, the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is:
1. \(5\) ms–1
2. \(8\) ms–1
3. \(10\) ms–1
4. \(12\) ms–1
The distance between two particles is decreasing at the rate of \(6\) m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of \(4\) m/sec. It can be concluded that particles' speeds could be:
1. \(5\) m/sec, \(1\) m/sec
2. \(4\) m/sec, \(1\) m/sec
3. \(4\) m/sec, \(2\) m/sec
4. \(5\) m/sec, \(2\) m/sec
At a metro station, a girl walks up a stationary escalator in time \(t_1\)
1. \( \left(\mathrm{t}_1+\mathrm{t}_2\right) / 2\)
2. \( \mathrm{t}_1 \mathrm{t}_2 /\left(\mathrm{t}_2-\mathrm{t}_1\right)\)
3. \( \mathrm{t}_1 \mathrm{t}_2 /\left(\mathrm{t}_1+\mathrm{t}_2\right) \)
4. \( \mathrm{t}_1-\mathrm{t}_2\)
Two trains, each \(50\) m long, are travelling in the opposite direction with velocities \(10\) m/s and \(15\) m/s. The time of crossing is:
1. \(10\) sec
2. \(4\) sec
3. \(2\sqrt{3}\) sec
4. \(4\sqrt{3}\) sec