J J Science Academy

1) Velocity-time curves plotted for two bodies are straight lines passing through origin. The slope of v-t curve for two bodies X and Y is 3 and 2 respectively. In a given time interval, the ratio of displacement of X to that of Y is

1) $ \frac{9}{4} $2) $ \frac{4}{9} $3) $ \frac{2}{3} $4) $ \frac{3}{2} $

Hint: Slope of v-t curve = acceleration $ s \propto a $ $ \frac{s_{1}}{s_{2}}=\frac{a_{1}}{a_{2}}=\frac{3}{2} $

2) The area under speed-time graph gives

1) displacement of the body.2) acceleration of the body.3) distance travelled by the body.4) average speed of the body.

3) For a body moving with uniform acceleration along straight line, the variation of its velocity ( v ) with position ( x ) is best represented by

1)

2)

3)

4)

4) The x-t graph of a body, is as shown in the figure. Its velocity will be positive in the region

1) AB2) BC3) DE4) All of the above

5) The x -t graph of a body, is as shown in the figure, the acceleration will be negative in the region

1) AB2) CD3) DE4) All of the above

6) The $x-t$ graph of a body, is as shown in the figure, the acceleration could be zero in the region

1) CD2) AB3) BC4) All of the above

7) The x -t graph of a body, is as shown in the figure, the velocity of the body changes the direction of motion in the region

1) CD (2) AB2) BC (4) None of the above

8) A performs circular motion, with origin as the centre. Consider a point A , on the circular path on +X -axis. The displacement-time graph, with respect to this point will be

9) Area under curves in which of the following graphs cannot be negative?

1) speed-time2) velocity-time3) acceleration-time4) none of the above

10) Which one of the following time-displacement graph represents two moving objects P and Q with zero relative velocity?

1)

2)

3)

4)

11) The velocity-time graph for a body in motion is as shown in the figure. The acceleration of the particle is zero at

1) A2) B3) C (4) D

Hint: Velocity is constant at C , so $ a=0 $

12) The velocity-time graph for a body in motion is as shown in the figure. In the region BC, the acceleration is

1) zero2) positive.3) negative.4) first positive, then negative.

13) The velocity-time graph for a body in motion is as shown in the figure. Which region could the acceleration be negative?

1) AB2) CD3) DE4) beyond E

14) The velocity-time graph for a body in motion is as shown in the figure. The displacement would be negative in the region

1) AB (2) BD2) DE (4) beyond E

15) A particle moves along x -axis in such a way that its x -coordinate varies with time according to the equation $x=4-2 t+t^{2}$. The speed of the particle will vary with time as

1)

2)

3)

4)

Hint: $x=4-2 t+t^{2}$ $v=\frac{dx}{dt}=-2+2 t$ At $t=0, v=-2$ At $t=1, v=0$ At t>1, v goes on increasing.

16) A performs circular motion, with origin as the centre. Consider a point A , on the circular path on +X -axis. The displacement-time graph, with respect to this point will be

17) The velocity-time graph for a body in motion is as shown in the figure. The average acceleration of the body from A to E is

1) positive.2) negative.3) zero.4) cannot be determined.

18) Which graph represents uniform motion?

1)

2)

3)

4) both (1) and (2)

Hint: Uniform motion means uniform velocity or constant slope of s-t graph.

19) The displacement versus time graph for a body moving in a straight line is shown in figure. Which of the following regions represents the motion, when no force is acting on the body?

1) (1) ab (2) bc2) (3) cd (4) de

Hint: The portion BC is parallel to time axis. Therefore, displacement during this interval is zero. Hence no force is acting on the particle.

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

1) $1:2$2) $1:{\sqrt{3}}$3) ${\sqrt{3}}:1$4) $1:3$

Hint: $\frac{v_{A}}{v_{B}}=\frac{\tan \theta_{A}}{\tan \theta_{B}}=\frac{\tan 30}{\tan 60}=\frac{1}{\sqrt{3}}\times\frac{1}{\sqrt{3}}=\frac{1}{3}$

21) Velocity-time graph of a body is as shown in figure below. Acceleration of body at $t=3$ is

1) $7.5 m / s^{2}$2) $5 m / s^{2}$3) $10.5 m / s^{2}$4) $15.5 m / s^{2}$

Hint: $a=\frac{dv}{dt}=\frac{20-5}{4-2}=\frac{15}{2}=7.5 m / s^{2}$

22) Velocity-time graph of a body is as shown in figure below. Displacement of body from $t=2 s$ to $t=7 s$ is

1) 45 m2) 35 m3) 50 m4) 55 m

Hint: Displacement = Area under curve from t=2s to t=7s$ = \frac{1}{2}\times(20+5)\times2+\frac{1}{2}\times(3)\times(20) = 25+30 = 55 m $

23) Figure below shows the time-acceleration graph for a particle in rectilinear motion. The average acceleration in first twenty seconds is

1) $45 m / s^{2}$2) $40 m / s^{2}$3) $15 m / s^{2}$4) $20 m / s^{2}$

Hint: $a_{av}=\frac{area of acceleration - time graph}{time}=\frac{300}{20}=15 m / s^{2}$

24) A body is dropped from a certain height. It takes 4 sec to reach the ground. The displacement-time graph will be

1)

2)

3)

4)

Hint: $h=\frac{1}{2}gt^{2}=\frac{1}{2}\times10\times(4)^{2}=80 m$ As $h \propto t^{2} \Rightarrow$ Graph is parabola.

25) A body is dropped from a certain height. It takes 4 sec to reach the ground. The speed time graph will be

1)

2)

3)

4)

Hint: v}1=$v2 = at= 10 x 4=40 m/s$

26) A body is dropped from a certain height. It takes 4 sec to reach the ground. The speed-time graph from the time it is dropped, till it reaches its original position is

1)

2)

3)

4)

27) On displacement time graph, two straight lines make angle $60^{\circ}$ and $30^{\circ}$ with time axis. The ratio of the velocities represented by them is

1) $1:2$2) $1:3$3) $2:1$4) $3:1$

Hint: $\frac{v_{A}}{v_{B}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}=\frac{\tan 60}{\tan 30}=\frac{\sqrt{3}}{1/\sqrt{3}}=3$