Displacement in 2D Motion

Q.

State the work-energy theorem and prove it for a variable force.

Q. In a car race, car $A$ takes $20\text{s}$ less than car $B$ to finish. It passes the finishing point with speed $v$ more than that of car $B$. Assuming that both the cars start from rest and travel with a constant acceleration of $50{\text{m/s}}^2$ and $40{\text{m/s}}^2$ respectively, what is the value of $v$ ?

1. $620\text{m/s}$
2. $894\text{m/s}$
3. $682\text{m/s}$
4. $864\text{m/s}$

Q. Two particles A and B are moving in XY plane. Their positions vary with time $t$, according to relation
$x_A\left(t\right)=4t^2,x_B\left(t\right)=7$
$y_A\left(t\right)=3t,y_B\left(t\right)=3+4t^2$
Distance between these two particles at $t=1\text{s}$ is:-

1. $5\text{m}$
2. $3\text{m}$
3. $4\text{m}$
4. $\sqrt{12}\text{m}$

Q. An aeroplane moves $400\text{m}$ towards north, $300\text{m}$ towards west and then $1200\text{m}$ vertically upward, then its displacement from the initial position is

1. $1600\text{m}$
2. $1800\text{m}$
3. $1500\text{m}$
4. $1300\text{m}$

Q. The graph in figure given below represents the velocity-time graph of a particle, starting from rest at point $\text{P}$. Find the time when particle will reach point $\text{P}$ again.

1. $8\text{s}$
2. $10\text{s}$
3. $12\text{s}$
4. $16\text{s}$

Q. In a car race, car $A$ takes $20\text{s}$ less than car $B$ to finish. It passes the finishing point with speed $v$ more than that of car $B$. Assuming that both the cars start from rest and travel with a constant acceleration of $50{\text{m/s}}^2$ and $40{\text{m/s}}^2$ respectively, what is the value of $v$ ?

1. $620\text{m/s}$
2. $894\text{m/s}$
3. $682\text{m/s}$
4. $864\text{m/s}$

Q. A $0.098\text{kg}$ block slides down a frictionless track as shown (Assume no energy loss on the entire track)
The time taken by the block to move from A to C is

1. $\sqrt{\frac{3}{g}}$
2. $\sqrt{\frac{2}{g}}$
3. $\frac{1}{\sqrt{g}}$
4. $\frac{1+\sqrt{3}}{\sqrt{g}}$

Q. A $0.098\text{kg}$ block slides down a frictionless track as shown (Assume no energy loss on the entire track)
The time taken by the block to move from A to C is

1. $\sqrt{\frac{3}{g}}$
2. $\sqrt{\frac{2}{g}}$
3. $\frac{1}{\sqrt{g}}$
4. $\frac{1+\sqrt{3}}{\sqrt{g}}$