Applications of equations of motion

Q. A bike racer starting from rest is riding with constant angular acceleration on a circular track. The ratio of angular displacement of the cyclist during $5^{th}$ and $7^{th}$ second is given by

1. $7:9$
2. $4:5$
3. $9:13$
4. $8:10$

Q. Starting from 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 $s_1$ 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. $2s_1<s_2<4s_1$

Q. Two cars $A$ and $B$ are at rest and at the same point initially. If $A$ starts with uniform velocity of $40\text{m/s}$ and $B$ starts in the same direction with constant acceleration of $4{\text{m/s}}^2$ , then $B$ will catch $A$ after the time

1. $10\text{s}$
2. $20\text{s}$
3. $30\text{s}$
4. $35\text{s}$

Q. A body starts from rest and travels $s\text{m}$ in $2^{nd}$ second, then, acceleration is

1. $\frac{3s}{2}{\text{m/s}}^2$
2. $2s{\text{m/s}}^2$
3. $\frac{2s}{3}{\text{m/s}}^2$
4. $3s{\text{m/s}}^2$

Q. A particle, after starting from rest experiences constant acceleration for $20\text{seconds}$. If it covers a distance of $S_1$ in first $10\text{seconds}$ and distance $S_2$ in next $10\text{seconds}$, then

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

Q. A particle is thrown upwards with speed $v_0$. Find its speed when it reaches $2/3^{rd}$ of the maximum height.

1. $\frac{v_0}{\sqrt{2}}$
2. $\frac{2v_0}{3}$
3. $\frac{v_0}{\sqrt{3}}$
4. $\frac{v_0}{3}$

Q. You drop a ball from a window located on an upper floor of a building. It strikes the ground with a speed $V$. You now repeat the drop, but your friend down on the ground throws another ball upward at the same speed $V$, releasing his ball at the same moment at which you drop yours from the window. At some location, the balls pass each other. This location is:

1. At the halfway point between window and ground
2. Above halfway point
3. Below halfway point
4. Cannot be determined

Q. A person standing near the edge of the top of a building throws two balls $A$ and $B$. The ball $A$ is thrown vertically upwards and $B$ is thrown vertically downward with the same speed. The ball $A$ hits the ground with a speed $v_A$ and the ball $B$ hits the ground with a speed $v_B$. Then,

1. $v_A>v_B$
2. $v_A<v_B$
3. $v_A=v_B$
4. The relation between $v_A$ and $v_B$ depends on height of the building above the ground.

Q. A body starts from rest and moving with an acceleration $2{\text{ms}}^{–2}$. The velocity of the body when it covers a distance of $10\text{m}$ (in ${\text{ms}}^{–1}$) is

1. $\sqrt{98}$
2. $\sqrt{40}$
3. $\sqrt{20}$
4. $\sqrt{12}$

Q. If a train travelling at $72\text{kmph}$ is to be brought to rest in a distance of $200\text{metres}$, then its retardation should be

1. $20m{s}^{-2}$
2. $10m{s}^{-2}$
3. $2m{s}^{-2}$
4. $1m{s}^{-2}$