1st Equation of Motion

Q. In series with 20 ohm resistor a 5 henry inductor is placed. To the combination an e.m.f. of 5 volt is applied. What will be the rate of increase of current at t = 0.25 sec

1. e
2. e^–2
3. None of these
4. e^–1

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. 
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.

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

3. $4m{s}^{-2}$

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

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. $na$

2. $\sqrt{n}a$

3. $n^{2}a$

4. $n^{3}a$

Q.

Which of the following displacement time (x-t) graphs can possibly represent the one-dimensional motion of a particle?

1. 

2. 

3. 

4. 

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

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

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

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

Q. If velocity is increasing continuously, then acceleration is .

1. positive
2. negative
3. zero

Q. A ball crosses point p with speed 6 $m/s$ and returns same point p with speed 8 $m/s$ in 5 seconds. Assuming acceleration($a$) is uniform, find the magnitude of $a$

1. $\frac{8}{5}m/s^2$
2. $\frac{6}{5}m/s^2$
3. $\frac{5}{5}m/s^2$
4. $\frac{14}{5}m/s^2$

Q. Starting form rest a particle is first accelerated for time $t_1$ with constant acceleration $a_1$ and then stops in time $t_2$ with constant retardation $a_2$. Let $v_1$ be the average velocity in this case and $s_1$ be the total displacement. In the second case, it is accelerated for the same time $t_1$ with constant acceleration $2a_1$ and comes to rest with constant retardation $a_2$ in time $t_3$. If $v_2$ is the average velocity in this case and $s_2$ the total displacement. Then

1. $v_2=2v_1$
2. $2v_1<v_2<4v_1$
3. $s_2=2s_1$
4. $2s_1<s_2<4s_1$