Applications of equations of motion

Q. A scooter accelerates from rest for time $t_1$ at a constant rate ${\alpha }_1$ and then retards at constant rate ${\alpha }_2$ for time $t_2$ and comes to rest. The correct value of $\frac{t_1}{t_2}$ will be -

1. $\frac{{\alpha }_1+{\alpha }_2}{{\alpha }_2}$
2. $\frac{{\alpha }_2}{{\alpha }_1}$
3. $\frac{{\alpha }_1+{\alpha }_2}{{\alpha }_1}$
4. $\frac{{\alpha }_1}{{\alpha }_2}$

Q. A ball is thrown vertically downwards with speed $30\text{m/s}$ from the top of the tower of height $80\text{m}$. The speed of the ball with which it hits the grounds is $(g=10{\text{m/s}}^2)$

1. $40\text{m/s}$
2. $60\text{m/s}$
3. $50\text{m/s}$
4. $30\text{m/s}$

Q. A ball is thrown vertically downward with a velocity of $20\text{m/s}$ from the top of a tower. It hits the ground after some time with a velocity of $80\text{m/s}$. The height of the tower is :
$(g=10{\text{m/s}}^2)$

1. $340\text{m}$
2. $360\text{m}$
3. $300\text{m}$
4. $320\text{m}$

Q. A stone is released from the top of the tower of height $20\text{m}$. Then its final velocity just before touching the ground will be

1. $20\text{m/s}$
2. $40\text{m/s}$
3. $200\text{m/s}$
4. $400\text{m/s}$

Q. A car starts from rest and accelerates uniformly to a speed of $180\text{km/h}$ in $10\text{s}$. The distance covered by the car in this time interval is

1. $500\text{m}$
2. $250\text{m}$
3. $100\text{m}$
4. $200\text{m}$

Q. A man is $d$ distance behind a bus. The bus starts from rest and moves away from the man with an acceleration $a$. At the same time man starts running towards the bus with a constant velocity $v$. Which of the following options are correct?

1. the man catches the bus if $v\ge \sqrt{2ad}$
2. if man just catches the bus, the time of catching the bus will be $t=v/a$
3. if man just catches the bus, the time of catching the bus will be $t=2v/a$
4. the man will catch the bus if $v\ge \sqrt{ad}$

Q. A person throws vertically $10$ balls per second with the same velocity. He throws a ball whenever the previous one is at its highest point. The height to which the balls rise is

1. $10\text{m}$
2. $5\text{m}$
3. $5\text{cm}$
4. $10\text{cm}$

Q. A ball is thrown vertically upwards with speed $10{\text{ms}}^{-1}$ from the top of a tower. It hits the ground after some time with a speed of $50{\text{ms}}^{-1}$. The height of tower is $(g=10{\text{ms}}^{-2})$

1. $240\text{m}$
2. $120\text{m}$
3. $60\text{m}$
4. $80\text{m}$

Q. A body is projected vertically upward with speed $40m/s$. The distance travelled by the body in last 2 second of the journey is $[g=10m/s^2]$

1. $10\text{m}$
2. $5\text{m}$
3. $60\text{m}$
4. $15\text{m}$

Q. The acceleration of the particle moving in $x-$direction with an initial velocity $8\text{m/s}$ is $3{\text{m/s}}^2$. Find its velocity at $t=2s$.

1. $14\text{m/s}$
2. $20\text{m/s}$
3. $18\text{m/s}$
4. $60\text{m/s}$

Q. A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at $2\frac{m}{s^2}$. He reaches the ground with a speed of $3\frac{m}{s}$. At what height, did he bail out ?

1. 293 m
2. 111 m
3. 91 m
4. 182 m

Q. A truck has an initial velocity of $50\text{m/s}$. On the application of brakes truck stops at $200\text{m}$. The acceleration of the truck will be

1. $-12.5{\text{ms}}^{-2}$
2. $24.5{\text{ms}}^{-2}$
3. $-6.25{\text{ms}}^{-2}$
4. $6.25{\text{ms}}^{-2}$

Q. A ball thrown vertically upwards with a speed of $19.6{\text{ms}}^{-1}$ from the top of a tower returns to the earth in $6\text{s}$. Find the height of the tower.
(Take $g=9.8{\text{m/s}}^2$)

1. $27.8\text{m}$
2. $58.8\text{m}$
3. $70\text{m}$
4. $92\text{m}$

Q. A body is thrown vertically upwards with velocity u. The distance travelled by it in the fifth and the sixth seconds are equal. The velocity u is given by$(g=9.8m/s^2)$

1. 24.5 m/s
2. 49.0 m/s
3. 73.5 m/s
4. 98.0 m/s

Q. A particle starting from rest travels a distance x in first 2 seconds and a distance y in next two seconds, then

1. $y=x$
2. $y=2x$
3. $y=3x$
4. $y=4x$

Q. Two bodies A (of mass $1\text{kg})$ and B (of mass $3\text{kg})$ are dropped from heights of $16\text{m}$ and $25\text{m}$, respectively. The ratio of the time taken by them to reach the ground is

1. $\frac{4}{5}$
2. $\frac{5}{4}$
3. $\frac{12}{5}$
4. $\frac{5}{12}$

Q. Assume that a car is able to stop with a retardation of $8{\text{m/s}}^2$ and that a driver can react to an emergency in $0.5\text{sec}$. Calculate the overall stopping distance of the car for a speed of $72\text{km/hr}$ of the car

1. $25\text{m}$
2. $10\text{m}$
3. $35\text{m}$
4. $30\text{m}$

Q. A ball is thrown vertically downward with a velocity $u$ from the top of a tower. It strikes the ground with a velocity $5u$. The time taken by the ball to reach the ground is given by

1. $2.5u$
2. $\frac{2u}{g}$
3. $\frac{4u}{g}$
4. $5u$

Q. A stone dropped from a certain height reaches ground in $5\text{sec}$. If it is dropped and stopped for infinitesimal time interval at $t=3\text{s}$, then time taken by the stone to reach the ground is

1. $6\text{s}$
2. $6.5\text{s}$
3. $7\text{s}$
4. $7.5\text{s}$

Q. The acceleration of the particle moving in positive $x-$direction with an initial velocity of $10m/s$ is $3m/s^2$. Its velocity at $t=4sec$ is

1. $20m/s$
2. $22m/s$
3. $24m/s$
4. $18m/s$

Q. A car has an initial velocity of $60\text{m/s}$. On application of brakes the car stops after $300\text{m}$. The retardation (deceleration) of the car is

1. $5{\text{m/s}}^2$
2. $3{\text{m/s}}^2$
3. $6{\text{m/s}}^2$
4. $10{\text{m/s}}^2$

Q. The brakes applied to a bike produce retardation of $5{\text{m/s}}^2$. If the bike takes $4\text{s}$ to stop after the application of brakes, calculate the distance it travels during this time.

1. $40\text{m}$
2. $45\text{m}$
3. $35\text{m}$
4. $50\text{m}$

Q. A ball is thrown vertically upwards with velocity of $10\text{m/s}$ from the top of a tower. It returns to ground after some time with speed of $60\text{m/s}$. The height of the tower is

$(g=10{\text{m/s}}^2)$

1. $375\text{m}$
2. $175\text{m}$
3. $125\text{m}$
4. $225\text{m}$

Q. A sports car can accelerate uniformaly to a speed of $162$ km/h in 5 sec. Its maximum breaking retardation is $6m/s^2$. Minimum time in which it can travel 1 km starting from rest and ending at rest in seconds is?

Q. A ball is thrown vertically upwards from the top of a tower at 4.9 m/s. 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

Q. A ball at rest is dropped into a well. The water is at a depth $h$ from the surface. If the speed of sound is $c$, then the time after which the splash is heard will be

1. $h[\sqrt{\frac{2}{gh}}+\frac{1}{c}]$
2. $h[\sqrt{\frac{2}{gh}}-\frac{1}{c}]$
3. $h[\frac{2}{g}+\frac{1}{c}]$
4. $h[\frac{2}{g}-\frac{1}{c}]$

Q. An open lift is moving upwards with velocity 10 m/s. It has an upward acceleration of 2 m/s${}^2$. A ball is projected upwards with velocity 20 m/s relative to ground. Find the time when ball again meets the lift.

1. $\frac{4}{3}s$
2. $\frac{5}{3}s$
3. $\frac{5}{4}s$
4. $\text{None}$

Q.

A ball is in a hot air balloon that starts from rest at t = 0 and accelerates upwards at 2m/s². After 10s, the ball is dropped from the balloon.Draw ball's v - t graph:

1. 

2. 

3. 

4. 

Q. A balloon is moving vertically upward with a velocity of $5\text{m/s}$. When it is at a height of $h$, a body is gently released from it. If it reaches the ground in $3\text{s}$, the height of the balloon when the body is released is (Take $g=10{\text{m/s}}^2$)

1. $45\text{m}$
2. $60\text{m}$
3. $30\text{m}$
4. $15\text{m}$

Q. You drop a ball from a window located on an upper floor of a building. It strikes the ground with a speed $V$. You now repeat the drop, but your friend down on the ground throws another ball upward at the same speed $V$, releasing his ball at the same moment at which you drop yours from the window. At some location, the balls pass each other. This location is:

1. At the halfway point between window and ground
2. Above halfway point
3. Below halfway point
4. Cannot be determined