Second Equation of Motion

Q. When an object is thrown vertically upward, on reaching the highest point, its value of acceleration due to gravity would be.

1. $4.9m{s}^{-2}$
2. $9.8m{s}^{-2}\uparrow$
3. $9.8m{s}^{-2}\downarrow$
4. $0m{s}^{-2}$

Q.

A ball thrown vertically upwards with a speed of 19.6 m/s from the top of a tower returns to the earth in 6s. Find the height of tower :

1. 58 m

2. 60 m

3. 58.8 m

4. None of these

Q. An object is dropped from rest at a height of $150m$ and simultaneously another object is dropped from rest at a height of $100m$. What is the difference in their heights after $2s$ if both the objects drop with same accelerations? How does the difference in heights vary with time?

1. $30m$
2. $40m$
3. $50m$
4. $60m$

Q.

How do you determine the maximum height of a projectile?

Q.

Two round rain drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be

1. 
2. 2.5 cm per sec
3. 
4. 10 cm per sec

Q. A car starts from rest and moves along the x-axis with constant acceleration of $5m{s}^{-2}$ for $8seconds$. If it then continues with constant velocity, what distance will the car cover in $12seconds$ since it started from the rest?

1. $300m$
2. $310m$
3. $320m$
4. $400m$

Q. Question 2
A train is travelling at a speed of $90kmph$. Brakes are applied so as to produce a uniform acceleration of $-0.5m{s}^{-2}$. Find how far the train will go before it is brought to rest.

Q. A ball thrown vertically upwards with a speed of $20m{s}^{-1}$ from the top of a tower reaches the earth in $8s$. Find the height of the tower. Take $g=10m{s}^{-2}$

1. $120m$
2. $100m$
3. $60m$
4. $160m$

Q.

A wooden block of mass 10 g is dropped from the top of a cliff 100 m high. Simultaneously, a bullet of mass 10 g is fired from the foot of the cliffupward with a velocity of $100m{s}^{-1}$. At what time will the bullet and the block meet ?

1. $4s$
2. $3s$
3. $2s$
4. $1s$

Q. A body starts from the origin with an acceleration of $6m{s}^{-2}$ along the x-axis and $8m{s}^{-2}$ along the y-axis. Its distance from the origin after $4seconds$ will be

1. $128m$
2. $64m$
3. $80m$
4. $56m$

Q.

A particle starts to move from rest with an acceleration of 4 $\frac{m}{s^2}$ for 4 seconds. Find the distance travelled in $4^{th}$ second.

1. 32 m

2. 14 m

3. 10 m

4. 30 m

Q. Question 4
A racing car has a uniform acceleration of $4m{s}^{-2}$. What distance will it cover in 10 seconds after start?

Q.

A stone is dropped from a cliff. Find its speed after the stone has fallen from 100 m. Acceleration due to gravity$g=9.8\frac{m}{s^2}$

1. 44.2 m/s

2. 9.8 m/s

3. 24 m/s

4. 19.6 m/s

Q. Derive the law of conservation of momentum.

Q. Let there are three equal masses situated at the vertices of an equilateral triangle, as shown in figure. Now the particle A starts with a velocity $v1$ towards line AB, particle B starts with the velocity $v_2$ towards line BC and particle starts with velocity $v_3$ towards line CA. Find the displacement of the centre of mass of the three particles A, B and C after time t. What would it be the displacement of centre of mass if $v_1=v_2=v_3$?

1. $(v_1+v_2+v_3)t$
2. $\frac{(v_1+v_2+v_3)t}{2}$
3. $\frac{(v_1+v_2+v_3)t}{3}$
4. '0'

Q. A car initially at rest starts moving with uniform acceleration of $10m{s}^{-2}$ for $10seconds$. What is the total distance covered by the car?

1. $500m$
2. $200m$
3. $600m$
4. $100m$

Q. A train accelerates from zero to $20m{s}^{-1}$ in $15s$. Calculate the distance covered by the train in same time.

1. $159.6m$
2. $194.6m$
3. $150m$
4. $139.6m$

Q.

Starting from rest at the top of an inclined plane a body reaches the bottom in 4 seconds. In what time does the body cover one-fourth the distance starting from the top?

1. 1 s

2. 2 s

3. 3 s

4. 4 s

Q.

A bus decreases its speed from 100 km/h to 80 km/h in 5 s. Find the acceleration of the bus.

1. -1.2 $m/s^2$

2. -1.6 $m/s^2$

3. -1.112 $m/s^2$

4. -1.116 $m/s^2$

Q. An object is dropped from rest at a height of $150m$ and simultaneously another object is dropped from rest at a height of $100m$. What is the difference in their heights after $2s$ if both the objects drop under the same acceleration? How does the difference in heights vary with time?

Q.

A ball is thrown vertically upwards. Prove that its time of ascent is equal to the time of descent.

Q. Two scooters starting from rest accelerate uniformly at the same rate. Time taken by second scooter to travel is twice the time taken by the first scooter. Then the relation between the distance covered by the first scooter $\left(S_1\right)$ to that of the second scooter $\left(S_2\right)$ is

1. $S_1=S_2$
2. $S_1=2S_2$
3. $S_2=4S_1$
4. $S_2=3S_1$

Q. A car accelerates from 0 m/s to 20 m/s in 5 seconds. The acceleration of the car is $m/s^2$.

1. 4
2. 8
3. 100

Q.

If a body is thrown up with an initial velocity $u$ and covers a maximum height of $h$, then $h$ is equal to $\frac{u^2}{2g}$:

1. u²/2g

2. u/2g

Q.

If a body is thrown up with an initial velocity $u$ and covers a maximum height of h, then h is equal to $\frac{u^2}{2g}$.

1. u²/2g

2. u/2g

Q.

A ball thrown vertically upwards with a speed of 19.6 $m{s}^{-1}$ from the top of a tower, it returns to the earth in 6 s. Find the height of the tower. [Take g = 9.8 m ${\sec }^{-2}$ ]

1. 60

2. 58

3. 58.8

4. None of these

Q.

A ball thrown up vertically returns to the thrower after 12 seconds. Find
(i) velocity with which it was thrown up.

Q.

An ant moves along a circular thread with speed $10\frac{cm}{s}$. It covers one cycle in 10 minutes. Chintu is a naughty boy who cut the thread to make it a straight line and challenges ant to reach the end in half the time. What should be the constant acceleration that ant should maintain to complete his challenge?

1. (1/500) m/s²

2. (1/750) m/s²

3. (1/1000) m/s²

4. (1/1500) m/s²

Q.

A bullet is fired vertically with an initial velocity of 19.6 m/s.

(a) How high will it reach?

(b) What is the time taken to reach that height?

Q. A bus of $6m$ long starts moving with an acceleration of $2m{s}^{-2}$. A cyclist $90m$ behind the bus starts simultaneously towards the bus at $20m{s}^{-1}$. After what minimum time will he be able to overtake the bus?

1. $4s$
2. $8s$
3. $16s$
4. $12s$