Displacement in 2D

Q. A particle moves from A to B along the semicircular curve as shown in the figure. The ratio of distance covered by particle to its displacement is

1. $\frac{\pi }{2}$
2. $\frac{2}{\pi }$
3. $\frac{\pi }{4}$
4. $1:1$

Q. A particle moves along the path $ABCA$ with a constant speed starting from $A$. Part $BC$ is circular with centre at $A$. The magnitude of displacement (from $A$) versus time graph will be

1. 
2. 
3. 
4. 

Q. A particle is moving in $xy-$plane with $y=\frac{x}{2}$ and velocity along $x$ direction is $u_x=4-2t$. The correct options are

1. Initial velocities of $x$ and $y$ directions are negative.
2. Initial velocities of $x$ and $y$ directions are positive.
3. Motion is first retarded, then accelerated
4. Motion is first accelerated, then retarded.

Q. The equations of motion are applicable only when the body moves with uniform acceleration.

1. True
2. False

Q.

A river is flowing from west to east at a speed of 5 metres per minute. A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

1. Due north

2. ${30}^{\circ }$ east of north

3. ${30}^{\circ }$ west of north

4. ${60}^{\circ }$ east of north

Q. Draw a graph for acceleration against time for a uniformly accelerated motion. How can it be used to find the change in speed in a certain interval of time?

Q. A particle moves from A to B along the semicircular curve as shown in the figure. The ratio of distance covered by particle to its displacement is

1. $\frac{\pi }{2}$
2. $\frac{2}{\pi }$
3. $\frac{\pi }{4}$
4. $1:1$

Q. A particle moves from A to B along the semicircular curve as shown in the figure. The ratio of distance covered by particle to its displacement is

1. $\frac{\pi }{2}$
2. $\frac{2}{\pi }$
3. $1:1$
4. $\frac{\pi }{4}$

Q. The velocity-time graph of a car moving on a straight road is shown. Find the distance travelled by the car after the brakes are applied :

1. $20m$
2. $40m$
3. $60m$
4. $80m$

Q. A particle is moving in $xy-$plane with $y=\frac{x}{2}$ and velocity along $x$ direction is $u_x=4-2t$. The correct options are

1. Initial velocities of $x$ and $y$ directions are negative.
2. Initial velocities of $x$ and $y$ directions are positive.
3. Motion is first retarded, then accelerated
4. Motion is first accelerated, then retarded.

Q. A particle is performing S.H.M. starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of

1. $0rad$
2. $\frac{\pi }{4}rad$
3. $\frac{\pi }{2}rad$
4. $\pi rad$

Q. A object starts from rest at $t=0$ and accelerates at a rate given by $a=6t$. What is its displacement at any time $t$?

1. $t^2$
2. $t^3$
3. $3t^2$
4. $3t^3$