Derivation of three equations of motion

Q. An automobile moving at a speed of $72\text{km/h}$ is brought to rest in $2\text{s}$ by application of brakes. How much distance does the automobile cover in these $2\text{s}$?

1. $\text{25 m}$
2. $\text{20 m}$
3. $\text{15 m}$
4. $\text{10 m}$

Q. The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:

1. 
2. 
3. 
4. 

Q. Which of the following graphs gives the equation $x=v_{0}t+\frac{1}{2}a{t}^2$

1. 
2. 
3. 
4. None of these

Q. Which option is correct for equation of motion:

1. $v=u+at$
2. $s=ut+\frac{1}{2}a{t}^2$
3. $v^2=u^2+2as$
4. All of these

Q. Velocity of a particle is in negative direction with constant acceleration in positive direction. Then, match the following columns.

Column-I	Column-II
(a)	Velocity-time graph	(p)	Slope$\to$negative
(b)	Acceleration-time graph	(q)	Slope$\to$positive
(c)	Displacement-time graph	(r)	Slope$\to$zero
		(s)	$\left|Slope\right|\to$increasing
		(t)	$\left|Slope\right|\to$ decreasing
		(u)	$\left|Slope\right|\to$ constant

1. $(A\to q,u,B\to r,u,C\to p,t)$
2. $(A\to q,u,B\to r,u,C\to p,u)$
3. $(A\to q,u,B\to r,C\to p,t)$
4. $(A\to q,B\to r,u,C\to p,t)$

Q. The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:

1. 
2. 
3. 
4. 

Q.

A car is travelling with a constant speed of 5 m/s. suddenly superman comes and starts pushing from behind providing a constant acceleration of 5 m/$s^2$. Find the velocity of the car after 2 sec.

1. 10 m/s

2. 25 m/s

3. 15 m/s

4. 35 m/s

Q. Find the incorrect equation of motion.

1. $v=u+at$
2. $s=ut+\frac{1}{2}a{t}^2$
3. $v^2-u^2=2as$
4. $v^2+u^2=2as$

Q.

A bullet moving with a velocity of 200 cm/s penetrates a wooden block and comes to rest after traversing 4 cm inside it. What velocity is needed for travelling distance of 9 cm in same block?

1. 100 cm/s

2. 136.2 cm/s

3. 300 cm/s

4. 250 cm/s

Q. Find the incorrect equation of motion.

1. $v=u+at$
2. $s=ut+\frac{1}{2}a{t}^2$
3. $v^2-u^2=2as$
4. $v^2+u^2=2as$