1st Equation of Motion

Q. A ball is thrown vertically with a velocity of $5m/s$ towards the ground from the top of a building of height $10m$. What is the change in its speed, when the ball is about to hit the ground? Take $g=10m/s^2$.

Q.

A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t, the total distance travelled by the car is given by

1. $\frac{1}{2}\left(\frac{\alpha \beta }{\alpha +\beta }\right)t^2$

2. $\frac{1}{2}\left(\frac{\alpha +\beta }{\alpha \beta }\right)t^2$

3. $\frac{1}{2}\left(\frac{{\alpha }^2+{\beta }^2}{\alpha }\right)t^2$

4. $\frac{1}{2}\left(\frac{{\alpha }^2-{\beta }^2}{\beta }\right)t^2$

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 car, moving with a speed of $50km/hr$, can be stopped by brakes after at least $6m$. If the same car is moving at a speed of $100km/hr$, the minimum stopping distance is

1. $24m$
2. $22m$
3. $20m$
4. $8m$

Q. A body initially moving with a velocity of $5{\text{ms}}^{–1}$, attains a velocity of $25{\text{ms}}^{–1}$ in $5s$. The acceleration of the body is:
(Assume constant acceleration)

1. $8{\text{ms}}^{-2}$
2. $7{\text{ms}}^{-2}$
3. $4{\text{ms}}^{-2}$
4. $3{\text{ms}}^{-2}$

Q.

A car moving at a speed u is stopped in a certain distance when the brakes produce a deceleration a. If the speed of the car is nu, what must be the deceleration of the car to stop it in the same distance?

1. $\sqrt{n}a$

2. $na$

3. $n^{2}a$

4. $n^{3}a$

Q. A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its flight if the air resistance is not ignored? (Assume that magnitude of resistive force is constant )

1. 
2. 
3. 
4. 

Q. Car A and Car B starts from origin with speeds $54$ kmph and $72$ kmph respectively. Both starts from origin at the same time. Find the distance between A and B after $20$ minutes .

1. $54$ km
2. $30$ km
3. $24$ km
4. $47$ km

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. The acceleration of the particle moving in positive $x-$ direction with an initial velocity of $20\text{m/s}$ is $4{\text{m/s}}^2$. Its velocity at $t=5\text{sec}$ is

1. $22\text{m/s}$
2. $40\text{m/s}$
3. $30\text{m/s}$
4. $25\text{m/s}$

Q. The acceleration of a car moving in positive $x-$direction with an initial velocity of $6m/s$ is $4m/s^2$. Its velocity at $t=5sec$ is

1. $26m/s$
2. $28m/s$
3. $24m/s$
4. $22m/s$

Q.

Car A is moving with a speed of 36 km/h on a two-lane road. Two cars B and C, each moving with a speed of 54 km/h in opposite directions on the other lane are approaching car A. At a certain instant when the distance AB = distance AC = 1 km, the driver of car B decides to overtake A before C does. What must be the minimum acceleration of car B so as to avoid an accident?

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

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

3. $3m{s}^{-2}$

4. $4m{s}^{-2}$

Q. A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is $5m$, the number of balls thrown per minute is $(takeg=10\frac{m}{s^2})$

1. 30
2. 60
3. 90
4. 45

Q. A car accelerates from rest at a constant rate of $2m{s}^{-2}$ for some time. Then it retards at a constant rate of $4m{s}^{-2}$ and come to rest. It remains in motion for $6s$.

1. Its maximum speed is $8m{s}^{-1}$
2. It maximum speed is $6m{s}^{-1}$
3. It travelled a total distance of $24m$
4. It travelled a total distance of $18m$

Q. A car accelerates from rest at a constant rate α for some time, after which it decelerates at a constant rate $\beta$ and comes to rest. If the total time elapsed is t, then the maximum velocity acquired by the car is

1. $\left(\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }\right)t$
2. $\left(\frac{{\alpha }^2-{\beta }^2}{\alpha \beta }\right)t$
3. $\frac{(\alpha +\beta )t}{\alpha \beta }$
4. $\frac{\alpha \beta t}{\alpha +\beta }$

Q. Car A and Car B starts from origin with speeds $54$ kmph and $72$ kmph respectively. Both starts from origin at the same time. Find the distance between A and B after $20$ minutes .

1. $54$ km
2. $30$ km
3. $24$ km
4. $47$ km

Q. The acceleration of a car moving in positive $x-$direction with an initial velocity of $6m/s$ is $4m/s^2$. Its velocity at $t=5sec$ is

1. $26m/s$
2. $28m/s$
3. $24m/s$
4. $22m/s$