Position Time Graph

Q.

When is the object at rest?

1. t = 5 sec

2. t = 10 sec

3. t = 20 sec

4. t = 30 sec

Q. Figure shows the position of a particle moving along the $x-$ axis as a function of time. Which of the following is correct?

1. The particle has come to rest 6 times.
2. The maximum speed is at $t=6\text{s}$.
3. The velocity remains positive for $t=0$ to $t=6\text{s}$.
4. The average velocity for the total period shown is negative.

Q. Find the distance covered by a particle during the time interval $t=0$ and $t=6\text{s}$ for which the speed-time graph is shown in figure

1. $90\text{m}$
2. $60\text{m}$
3. $75\text{m}$
4. $50\text{m}$

Q. Figure shows $(x,t),(y,t)$ diagram of a particle moving in $2-$dimensions.

If the particle has a mass of $500\text{g}$, the force acting on the particle is (Assume $x=t,y=t^2$ are equation of given graphs)

1. $1\text{N}$ along $y-$ axis
2. $1\text{N}$ along $x-$ axis
3. $0.5\text{N}$ along $x-$ axis
4. $0.5\text{N}$ along $y-$ axis

Q. Compare the speed of the three particles $A,B$ and $C$ as per the distance-time graph shown below.

1. $v_A>v_B>v_C$
2. $v_A>v_C>v_B$
3. $v_B>v_A>v_C$
4. $v_C>v_A>v_B$

Q. X-Y plot of a body undergoing motion in 2 dimensions is a photograph of the actual motion.

1. False
2. True

Q. Starting at time $t=0$ from the origin with speed $1{\text{ms}}^{-1}$, a particle follows a two-dimensional trajectory in the $x-y$ plane so that its coordinates are related by the equation $y=\frac{x^2}{2}$. The $x$ and $y$ components of its acceleration are denoted by $a_x$ and $a_y$, respectively. Then

1. $a_x=0$ implies that at $t=1\text{s}$, the angle between the particle’s velocity and the $x$ axis is ${45}^{\circ }$
2. $a_x=0$ implies $a_y=1{\text{ms}}^{-2}$ at all times
3. at $t=0$, the particle’s velocity points in the $x-$direction
4. $a_x$ = $1{\text{ms}}^{-2}$ implies that when the particle is at the origin, $a_y=1{\text{ms}}^{-2}$

Q.

What is the distance of the body from the starting point at t = 30 s?

What is the distance of the body from the starting point at t = 30 s?

1. 10 m

2. 0 m

3. 20 m

4. -10 m

Q. What does the slope of the coloured lines express in this position time graph.

1. ${\overrightarrow{v}}_{inst}$
2. $\overrightarrow{v}=0$
3. ${\overrightarrow{v}}_{avg}$

Q.

The displacement-time graph for two particles A and B are straight lines inclined at angles of ${30}^{\circ }$ and ${60}^{\circ }$ with the time axis. The ratio of velocities of $v_A$ : $v_B$ is

1. 1 : 2

2. 1 : $\sqrt{3}$

3. $\sqrt{3}$ : 1

4. 1 : 3

Q. A particle at rest is projected from the origin moves in $x-y$ plane with a velocity of $\overrightarrow{v}=(3\hat{i}+6x\hat{j})\text{m/s}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along $+x$ and $+y$ axis. Which of the following equations represent the equation of path followed by the particle?

1. $y=x^2$
2. $y=\frac{1}{x^2}$
3. $y=2x^2$
4. $y=\frac{1}{x}$

Q.

The displacement versus time curve is given below. Match the nearest option. (Assuming curves to be parabolic)


$\begin{array}{cc}\text{Column I}& \text{Column II}\\ i.OA& \text{a. velocity increase with time linearly}\\ ii.AB& \text{b. velocity decreases with time}\\ iii.BC& \text{c. velocity is independent of time}\\ iv.CD& \text{d. velocity is zero}\end{array}$

1. $i.\to a.,ii.\to c.,iii.\to b.,iv.\to d$.
2. $i.\to a.,ii.\to c.,iii.\to d.,iv.\to b$.
3. $i.\to c.,ii.\to a.,iii.\to b.,iv.\to d$.
4. $i.\to a.,ii.\to b.,iii.\to c.,iv.\to d$.

Q. Figure shows $(x,t),(y,t)$ diagram of a particle moving in $2-$dimensions.

If the particle has a mass of $500\text{g}$, the force acting on the particle is (Assume $x=t,y=t^2$ are equation of given graphs)

1. $1\text{N}$ along $y-$ axis
2. $1\text{N}$ along $x-$ axis
3. $0.5\text{N}$ along $x-$ axis
4. $0.5\text{N}$ along $y-$ axis

Q. A particle is moving along $x-$axis. Its $x-$coordinate versus time graph is shown.


Its $v-t$ graph will be:

1. 
2. 
3. 
4. 

Q.

What is the total distance travelled till 30 seconds?

1. -10 m

2. 40 m

3. 10 m

4. 30 m