Distance Time Graph

Q. Explain the concept of rain-man problem in relative velocity.

Q. Identify the incorrect displacement-time curve which does not represent motion in one dimension.

1. 
2. 
3. 
4. 

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 train of $150m$ in length is going towards the north direction at a speed of$10m/s.$ A parrot flying at the speed of $5m/s$ towards the south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to

Q. The displacement-time graph of a moving object is shown in Figure. Which of the following velocity-time graphs could represent the motion of the same body?

1. 
2. 
3. 
4. 

Q. For the displacement-time graph shown in figure, the ratio of the magnitudes of the velocities during the first two second and the next four second is

1. 1 : 1
2. 3 : 2
3. 2 : 1
4. 1 : 2

Q.

Which of the following graphs cannot possibly represent one dimensional motion of a particle?

1. I

2. II

3. III and IV

4. All

Q. The displacement of a particle as a function of time is shown in the figure. It indicates

1. the particle starts with a certain velocity, but the motion is retarded and finally the particle stops.
2. the velocity of the particle decreases.
3. the acceleration of the particle is in opposite direction to the velocity.
4. the particle starts with a constant velocity, the motion is accelerated and finally the particle moves with another constant velocity.

Q. If a particle moves with a constant speed the distance time graph will look like??

Q.

Give an example of a body moving with uniform speed and constant acceleration.

Q. The velocity time graph of the motion of the body is shown in the figure. The total displacement travelled by the body during the motion is

1. $\frac{1}{2}(AD+BE)\times OC$
2. $\frac{1}{2}(OA+BC)\times OC$
3. $\frac{1}{2}(OC+AB)\times AD$
4. $\frac{1}{2}(OA+AB)\times BC$

Q. Assertion: In the $s–t$ graph shown in the figure, the velocity of the particle is negative and acceleration is positive.

Reason: The slope of $s–t$ graph is negative and increasing in magnitude.

1. Both assertion and reason are correct and reason is the correct explanation of assertion.
2. Both assertion and reason are correct and reason is not the correct explanation of assertion.
3. Assertion is true but reason is false.
4. Assertion is false but reason is true.

Q.

Figure 3.23 gives the x-t plot of a particle executing one-dimensional simple harmonic motion. (You will learn about this motion in more detail in Chapter14). Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, – 1.2 s.

(Fig: 3.23)

Q.

An object at rest at the origin begins to move in the +x direction with a uniform acceleration of 1 m/s${}^2$ for 4 s and then it continues moving with a uniform velocity of 4 m/s in the same direction. The x - t graph for object's motion will be

1. 

2. 

3. 

4. 

Q.

Suppose the platform of the previous problem is brought to rest with the ball in the hand of the kid standing on the rim. The kid throws the ball horizontally to his friend in a direction tangential to the rim with a speed v as seen by his friend. Find the angular velocity with which the platform will start rotating.

Q. A particle moves, along a straight line OX. At a time $t$ (in second), the position $x$ (in metre) of the particle from $O$ is given by $x=40+12t-t^3$. How much distance particle covers before coming to rest?

1. $16\text{m}$
2. $40\text{m}$
3. $24\text{m}$
4. $56\text{m}$

Q. A train running at $30m/s$ comes to rest at uniform deceleration within $44s$. The distance travelled by train before coming to rest is

1. $654m$
2. $612m$
3. $660m$
4. $630m$

Q.

Look at the graphs (a) to (d) (Fig. 3.20) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle.

a)


b)



c)


d)

Q. Figure (i) and (ii) below shows the parabolic displacement time graphs of two particles moving along the x-axis. We can say that

1. both the particles are speeding up.
2. particle (i) is speeding down while particle (ii) is speeding up.
3. both the particles are speeding down.
4. particle (i) is speeding up while particle (ii) is speeding down.

Q. Displacement - time graph of a body travelling in a straight line is shown in the figure.

Velocity-time graph for the motion of the body will be

1. 
   
2. 
3. 
4. 

Q. What can you say about the nature of motion of a body if its displacement-time graph is a straight line parallel to time axis ?

1. body is stationary (or no motion)
2. body has non zero acceleration
3. body has non zero velocity
4. None of the above

Q. A physical quantity $Z$ as a function of time is given as $Z\left(t\right)=A^{\frac{3}{2}}{e}^{–kt},$ where $k=0.1s^{–1}$. The measurement of A has an error of $2.00\%.$ If the error in the measurement of time is $1.25\%,$ then the percentage error in the value of $Z\left(t\right)$ at $t=10s$ would be

1. $2.50\%$
2. $3.50\%$
3. $3.75\%$
4. $4.25\%$

Q. Following graphs show the motion of a body. Pick the odd graph which does not conform to the motion of the body.

1. 
2. 
3. 
4. 

Q. A particle shows distance $-$ time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point.

1. D
2. A
3. B
4. C

Q. Comment on the graph shown below.

1. Velocity of the particle is constant.
2. This is impossible graph.
3. Velocity of the particle is decreasing.
4. Velocity of the particle is negative.

Q. Refer to distance $\left(x\right)-$ time $\left(t\right)$ graph. Which of the following is incorrect?

1. At D, velocity is positive.
2. At F, motion is in the -x direction.
3. At C, velocity is +ve
4. All of these

Q. The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown in figure. During the interval $OA,AB,BC$ and $CD$, the acceleration of the particle is

1. $\begin{array}{cccc}OA& AB& BC& CD\\ +& 0& +& +\end{array}$
2. $\begin{array}{cccc}OA& AB& BC& CD\\ -& 0& +& 0\end{array}$
3. $\begin{array}{cccc}OA& AB& BC& CD\\ +& 0& -& +\end{array}$
4. $\begin{array}{cccc}OA& AB& BC& CD\\ -& 0& -& 0\end{array}$

Q. The graph between the displacement $x$ and time $t$ for a particle moving in a straight line is shown in figure. During the interval $OA,AB,BC$ and $CD$, the acceleration of the particle is

1. $\begin{array}{cccc}OA& AB& BC& CD\\ -& 0& +& 0\end{array}$
2. $\begin{array}{cccc}OA& AB& BC& CD\\ +& 0& -& +\end{array}$
3. $\begin{array}{cccc}OA& AB& BC& CD\\ +& 0& +& +\end{array}$
4. $\begin{array}{cccc}OA& AB& BC& CD\\ -& 0& -& 0\end{array}$

Q.

Look at the graphs (a) to (d) (Fig. 3.20) carefully and state, with reasons, which of these cannot possibly represent one-dimensional motion of a particle.

(a)

(b)

(c)

(d)

Q.

A body changes its position according to the relation

x=2+6t

What is the shape of the position-time graph of the body? What will be the intercept on the x-axis assuming x to be in meters and t in seconds?