3rd Equation of Motion

Q. A car starting from rest accelerates at the rate $f$ through a distance $s$, then continues at constant speed for time $t$ and then decelerates at rate $\frac{f}{2}$ to come to rest. If the total distance covered is $15s$, then which one is correct?

1. $s=\frac{f{t}^2}{72}$
2. $s=\frac{f{t}^2}{4}$
3. $s=\frac{f{t}^2}{6}$
4. $s=\frac{f{t}^2}{2}$

Q. An alpha particle enters a hollow tube of 4 m length with an initial speed of $1\frac{km}{s}$. It is accelerated in the tube and comes out of it with a speed of $9\frac{km}{s}$. The time for which it remains inside the tube is

1. $8\times {10}^{-3}s$
2. $80\times {10}^{-3}s$
3. $800\times {10}^{-3}s$
4. $8\times {10}^{-4}s$

Q. A car, starting from rest, accelerates at the rate f through a distance S, then continuous at constant speed for time t and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 s, then

1. $S=\frac{1}{2}f{t}^2$
2. $S=\frac{1}{4}f{t}^2$
3. $S=\frac{1}{72}f{t}^2$
4. $S=\frac{1}{6}f{t}^2$

Q. A bullet emerges from a gun barrel of length $1.2m$ with a speed of $640m/s$. Assuming constant acceleration, the approximate time that it spends in the barrel after the gun is fired is

1. $3.75\times {10}^{-3}s$
2. $4.5\times {10}^{-3}s$
3. $5\times {10}^{-3}s$
4. $1.75\times {10}^{-3}s$

Q. A body moving in a straight line with constant acceleration of $10{\text{ms}}^{-2}$ covers a distance of $40\text{m}$ in the $4^{th}$ second. How much distance will it cover in the $6^{th}$ second?

1. $50\text{m}$
2. $60\text{m}$
3. $70\text{m}$
4. $80\text{m}$

Q. Stopping distance of a moving vehicle is directly proportional to

1. square of the initial velocity.
2. square of the initial acceleration.
3. the initial velocity.
4. the initial accleration.

Q. A car, starting from rest, accelerates at the rate f through a distance S, then continuous at constant speed for time t and then decelerates at the rate $\frac{f}{2}$ to come to rest. If the total distance traversed is 15 s, then

1. $S=\frac{1}{2}f{t}^2$
2. $S=\frac{1}{4}f{t}^2$
3. $S=\frac{1}{72}f{t}^2$
4. $S=\frac{1}{6}f{t}^2$

Q. For a car moving on a straight line with initial speed $u$, the minimum distance over which it can be stopped is $s$. If it's initial speed becomes $nu$, what will be the minimum distance over which it can be stopped? Assume constant braking force.

1. $\frac{s}{n}$
2. $\frac{s}{n^2}$
3. $ns$
4. $n^{2}s$

Q. A body travels for $15sec$ starting from rest with constant acceleration. If it travels distances $s_1,s_2$ and $s_3$ in the first five seconds, second five seconds and next five seconds respectively, the relation between $s_1,s_2$ and $s_3$ is

1. $s_1=\frac{1}{3}{s}_2=\frac{1}{5}{s}_3$
2. $s_1=\frac{1}{5}{s}_2=\frac{1}{3}{s}_3$
3. $2s_1=\frac{1}{3}{s}_2=\frac{1}{5}{s}_3$
4. $s_1=\frac{1}{6}{s}_2=\frac{1}{5}{s}_3$

Q. A car has an initial velocity of $60\text{m/s}$. On application of brakes the car stops after $300\text{m}$. The retardation (deceleration) of the car is

1. $5{\text{m/s}}^2$
2. $3{\text{m/s}}^2$
3. $6{\text{m/s}}^2$
4. $10{\text{m/s}}^2$

Q. If a car travelling at $40\text{m/s}$ is to be brought to rest in a distance of $100\text{m}$, then its retardation should be

1. $6{\text{m/s}}^2$
2. $8{\text{m/s}}^2$
3. $10{\text{m/s}}^2$
4. $9{\text{m/s}}^2$

Q. A body starts from rest and moving with an acceleration $5{\text{ms}}^{–2}$. The velocity of the body when it covers a distance of $100\text{m}$ (in ${\text{ms}}^{–1}$) is

1. $2\sqrt{10}{\text{ms}}^{–1}$
2. $10\sqrt{2}{\text{ms}}^{–1}$
3. $10\sqrt{10}{\text{ms}}^{–1}$
4. $10{\text{ms}}^{–1}$

Q. A truck has an initial velocity of $50\text{m/s}$. On the application of brakes truck stops at $200\text{m}$. The acceleration of the truck will be

1. $-12.5{\text{ms}}^{-2}$
2. $24.5{\text{ms}}^{-2}$
3. $-6.25{\text{ms}}^{-2}$
4. $6.25{\text{ms}}^{-2}$

Q. A train starts from rest and its speed increases at a constant rate $\alpha$ to $v$ and then remains constant for an interval and finally decreases to zero at a constant rate $\beta$. The total distance travelled by train is $l$. The time taken to complete the journey is $t$. Then,

1. $t=\frac{l(\alpha +\beta )}{\alpha \beta }$
2. $t=\frac{l}{v}+\frac{v}{2}(\frac{1}{\alpha }+\frac{1}{\beta })$
3. $\text{t is minimum when v}=\sqrt{\frac{2t\alpha \beta }{(\alpha -\beta )}}$
4. $\text{t is minimum when v}=\sqrt{\frac{2l\alpha \beta }{(\alpha +\beta )}}$

Q. A particle is thrown vertically upwards. Its velocity at half of the maximum height is $20\text{m/s}$. Then the maximum height attained by it will be: (Take $g=10{\text{m/s}}^2$)

1. $40\text{m}$
2. $25\text{m}$
3. $10\text{m}$
4. $45\text{m}$

Q. A particle is thrown vertically upwards. Its velocity at half of the maximum height is $20\text{m/s}$. Then the maximum height attained by it will be: (Take $g=10{\text{m/s}}^2$)

1. $40\text{m}$
2. $25\text{m}$
3. $10\text{m}$
4. $45\text{m}$

Q.

A train is travelling at the speed of 180 km/hr. In order to trap superman Lex Luthor has broken the tracks. Unware of Luthor's evil intensions, superman tries to stop the train by pushing it in opposite direction.Right at the moment when the train is 300 m away from the crack in the track, Superman is applying a deceleration of 5 m/$s^2$. Just after 2 sec a bullet laced with kryptonite hits superman which incapacitates him for a while. How long has super man got to remove the bullet and start to give deceleration so to protect the innocents? (Trains brake system has failed)

1. 1s

2. 2s

3. 1.25s

4. 0s

Q. Speeds of two identical cars are $u$ and $4u$ at a specific instant. If the same deceleration is applied on both the cars, the ratio of the respective distances in which the two cars are stopped from that instant is

1. $1:1$
2. $1:4$
3. $1:8$
4. $1:16$

Q. A body moving in a straight line with constant acceleration of $10{\text{ms}}^{-2}$ covers a distance of $40\text{m}$ in the $4^{th}$ second. How much distance will it cover in the $6^{th}$ second?

1. $50\text{m}$
2. $60\text{m}$
3. $70\text{m}$
4. $80\text{m}$

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. If the velocity of a particle is given by $v=(180-16x{)}^{\frac{1}{2}}m/s$ then its acceleration will be

1. $Zero$
2. $8m/s^2$
3. $-8m/s^2$
4. $4m/s^2$

Q. A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball at $\frac{T}{3}$ second?

1. $\frac{8h}{9}$ meters from the ground
2. $\frac{7h}{9}$ meters from the ground
3. $\frac{h}{9}$ meters from the ground
4. $\frac{17h}{18}$ meters from the ground

Q. The driver of a car moving at a speed of 10 m/s applies breaks after noticing an obstacle. Retardation due to the breaks is $4m/s^2$. Distance travelled by the car in 3 seconds after applying breaks is

1. 12 m
2. 12.5 m
3. 10 m
4. 11 m

Q. For a car moving on a straight line with initial speed $u$, the minimum distance over which it can be stopped is $s$. If it's initial speed becomes $nu$, what will be the minimum distance over which it can be stopped? Assume constant braking force.

1. $\frac{s}{n}$
2. $\frac{s}{n^2}$
3. $ns$
4. $n^{2}s$

Q. Speeds of two identical cars are $u$ and $4u$ at a specific instant. If the same deceleration is applied on both the cars, the ratio of the respective distances in which the two cars are stopped from that instant is

1. $1:1$
2. $1:4$
3. $1:8$
4. $1:16$

Q. If a body looses half of its velocity on penetrating $3\text{cm}$ in a wooden block, then how much will it penetrate more before coming to rest?

1. $1\text{cm}$
2. $2\text{cm}$
3. $3\text{cm}$
4. $4\text{cm}$