Equations of Motion

Q. Question 4
If the displacement of an object is proportional to square of time, then the object moves with
(a) uniform velocity
(b) uniform acceleration
(c) increasing acceleration
(d) decreasing acceleration

Q.

A stone is thrown vertically upwards with a speed of 20 m/s. How high will it go before it begins to fall? $(g=9.8m/s^2)$

Q.

A stone is released from the top of a tower of height $19.6m$. Calculate its final velocity just before touching the ground.

Q.

A stone is allowed to fall from the top of a tower $100\hspace{0.17em}\text{m}$ high and at the same time, another stone is projected vertically upwards from the ground with a velocity of $25\frac{\text{m}}{\text{s}}$. Calculate when and where the two stones will meet.

Q.

A ball is thrown up and is caught by the player after 4 seconds. How high did it go and with what velocity was it thrown? How far below the ball will be from its highest point after 3 seconds from start?

Q.

Two bodies of different masses $m_a$ and $m_b$ are dropped from two different heights $a$ and $b.$ The ratio of the time taken by the two to cover these distances are

1. $a:b$

2. $b:a$

3. $\sqrt{a}:\sqrt{b}$

4. $a^2:b^2$

Q.

A stone falls from a building and reaches the ground 2.5 seconds later. How high is the building ? $(g=9.8m/s^2)$

Q. A car moving with initial velocity of $15m{s}^{-1}$ accelerates at the rate of $4m{s}^{-2}$. What is the final velocity of the car after $10s$?

1. $65m{s}^{-1}$
2. $40m{s}^{-1}$
3. $55m{s}^{-1}$
4. $70m{s}^{-1}$

Q.

A ball thrown vertically upwards with a speed of $20m/s$ from the top of a tower reaches a certain height and then falls back to the earth in $6s.$ Find the height of the tower. [Take acceleration due to gravity, $g=10m/s^2$]

1. $100m$

2. $150m$

3. $160m$

4. None of these

Q.

A bullet moving with 10 m/s hits a wooden plank. The bullet stops after penetrating the plank 2 cm deep. Calculate the retardation of the bullet.

Q.

A stone is dropped from a height of 20 m.
(i) How long will it take to reach the ground ?
(ii) What will be its speed when it hits the ground ? $(g=10m/s^2)$

Q.

When a cricket ball is thrown vertically upwards, it reaches a maximum height of 5 metres.
(a) What was the initial speed of the ball ?
(b)) How much time is taken by the ball to reach the highest point ? $(g=10m{s}^{-2})$

Q.

A man is moving with 36 kmph. The time of reaction is 0.9 seconds. On seeing an obstacle in the path, he applies brakes and decelerates at 5 m/s², the total distance covered before he stops is:

1. 18 m

2. 17 m

3. 16 m

4. 19 m

Q.

A body is thrown vertically up with a velocity 98 m/s. How much high it will rise ? (g = 9.8 $m/s^2$). Give your answer in metres.

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Q. A stone is released from the top of a tower of height 78.4 m. Find the time taken by the stone to reach the ground.

Q.

The average time taken by a normal person to react to an emergency is one fifteenth of a second and is called reaction time. The reaction time of people increases when they are intoxicated. If a bus is moving with a velocity of 90km/hr and its driver sees a child running across the road, how much distance had the bus moved if the reaction time of driver was ½ second under the influence of alcohol?

Q.

A balloon starts from the ground and moves vertically upwards with an acceleration of 2
m/s2
. After 5s, a stone is released from the balloon. Find the time taken by the stone to reach the
ground

Q.
Acceleration time graph of particle moving in straight line is given. If initial velocity of particle is 2m/s. Its velocity at $4^{th}$ sec is

Q. The velocity-time graph for a car is given below. Calculate the total distance and net displacement covered by the car in the entire journey.

1. 175m, 50m
2. 225m, 125m
3. 50m, 175m
4. 125m, 225m

Q.

Question 25
Two objects of masses $m_1$ and $m_2$ having the same size are dropped simultaneously from heights $h_1$ and $h_2$ respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if (i) one of the objects is hollow and the other one is solid and (ii) both of them are hollow, size remaining the same in each case. Give reason.

Q.

The stone is thrown vertically upwards and the height $x$ feet reached by the stone in $tsec$, is given by $x=80t-16t^2$. the stone reaches the maximum height in

1. $2\mathrm{s}$

2. $2.5\mathrm{s}$

3. $3\mathrm{s}$

4. $1.5\mathrm{s}$

Q.

Describe the motion of the body which is accelerating at a constant rate of 10 m s^-2 _{​​​​​​.} If the body starts from the rest how much distance will it cover in 2 sec

Q.

An object is thrown vertically upwards with a velocity is \mu, the greatest height It to which it will rise before falling back is given by :
(a) $\mu /g$
(b) ${\mu }^2/2g$
(c) ${\mu }^2/g$
(d) $\mu /2g$

Q.

A body moving with a constant acceleration a possesses some initial velocity u.What will be its velocity after it has covered certain distance S ?

Q.

A man is moving with 36 kmph. On seeing an obstacle in the path, he applies brakes and decelerates at 5 m/s2, if the time of reaction is 0.9 seconds. Then the total distance covered before he stops is:

1. 17 m

2. 16 m

3. 19 m

4. 18m

Q.

A ball is thrown up and attains a maximum height of $19.6m$. Its initial speed was :

1. $9.8m{s}^{-1}$

2. $44.3m{s}^{-1}$

3. $19.6m{s}^{-1}$

4. $98m{s}^{-1}$

Q.

A ball thrown up is caught back by the thrower after $6s$. Calculate (i) the velocity with which the ball was through up, (ii) the maximum height attained by the ball, and (iii) the distance covered by the ball after $2s$. $(Take,g=9.8m{s}^{-2})$

Q. Question 14
A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity.

Q. Define force. Derive the formula for force.

Q.

A toy car is powered by water and compressed air. When the car is fully pumped up and released, it accelerates at 2 $m{s}^{-2}$ for 3 seconds. As soon as this water runs out the car begins to slow down. The car travels 27 meters before coming to rest. What is its rate of acceleration when stopping and what is the total time of the motion?

1. a = - 2 , t = 6 s

2. a = - 1 , t = 9 s

3. a = - 2 , t = 9 s

4. a = - 1 , t = 6 s