J J Science Academy - Practice Test

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) AB 2) BC 3) DE 4) 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) AB 2) CD 3) DE 4) 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) CD 2) AB 3) BC 4) 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) AB 3) 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

1)

2)

3)

4)

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

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

1) speed-time 2) velocity-time 3) acceleration-time 4) 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). Figure shows v-t graphs. For which graph is displacement maximum?

1) a 2) b 3) c 4) d

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

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

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

13). The velocity-time graph for a body in motion is as shown in the figure. The direction of velocity changes at

1) D 2) B 3) C 4) both (1) and (2)

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

1) zero 2) positive. 3) negative. 4) first positive, then negative.

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

1) AB 2) CD 3) DE 4) beyond E

16). 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) BD 3) DE 4) beyond E

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

1)

2)

3)

4)

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

19). 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.

20). 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) ab 2) bc 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.

21). 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: $$\frac{v_A}{v_B}=\frac{\tan \theta_A}{\tan \theta_B}=\frac{\tan 30}{\tan 60}=\frac{1}{\sqrt{3}} \times \frac{1}{\sqrt{3}}=\frac{1}{3}$$

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

23). 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 m 2) 35 m 3) 50 m 4) 55 m

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

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

25). 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: $$h=\frac{1}{2}gt^2=\frac{1}{2} \times 10 \times (4)^2=80 m$$ As $(h \propto t^2)$ \Rightarrow Graph is parabola.

26). 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: $(v = at = 10 \times 4 = 40 m/s)$

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

1)

2)

3)

4)

28). A particle moves along X -axis in such a way that its x -coordinate varies with time t according to the equation: x $(=(8+8t+4t^2) m)$. The velocity of the particle will vary with time according to the graph

1)

2)

3)

4)

Hint: $$x=8+8t+4t^2$$ $$v=\frac{dx}{dt}=8+8t$$

29). The displacement-time graph of a body is as shown in the figure. The body experiences positive acceleration in the region

1) AB 2) BC 3) CD 4) nowhere on graph

30). 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: $$\frac{v_A}{v_B}=\frac{\tan \theta_1}{\tan \theta_2}=\frac{\tan 60}{\tan 30}=\frac{\sqrt{3}}{1 / \sqrt{3}}=3$$

31). A lift is going up. The variation in the speed of the lift is as given in the graph. What is the height to which the lift takes the passengers?

1) 3.6 m 2) 28.8 m 3) 36.0 m 4) cannot be calculated from the above graph.

Hint: Height to which the passengers are taken by the lift = Distance covered by the lift = Area under velocity-time graph = $(\frac{3.6 \times (12+8)}{2}=36 m)$

32). The velocity ( v ) - time ( t ) graph of a body in a straight line is as shown in the figure. The displacement of the body in five seconds is

1) 2 m 2) 3 m 3) 4 m 4) 5 m

Hint: Displacement = Area under curve with sign = $(\frac{1}{2} \times 2 \times 3) - (1 \times 2 \times 1) + (1 \times 1) = 3 - 1 + 1 = 3 m)$

33). A particle starts from rest. Its acceleration $(a)$ versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be

1) $(110 m/s)$ 2) $(55 m/s)$ 3) $(550 m/s)$ 4) $(660 m/s)$

Hint: The area under the acceleration-time graph gives change in velocity. Since, particle starts with $(u=0)$, therefore Change in velocity = area under a-t graph $$\frac{1}{2} \times 10 \times 11$$ $$v_{max} - 0 = 55 m/s$$

34). Figure shows the time-displacement curve of the particles P and Q . Which of the following statement is CORRECT?

1) Both P and Q move with uniform equal speed. 2) P is accelerated Q is retarded. 3) Both P and Q move with uniform speeds but the speed of P is more than the speed of Q . 4) Both P and Q move with uniform speeds but the speed of Q is more than the speed of P.

Hint: As $((\text{Slope})_P > (\text{Slope})_Q \Rightarrow V_P > V_Q)$

35). The speed of a car as a function of the time is shown in the figure given below. The distance travelled by the car is

1) 160 m in 8 sec . 2) 80 m in 8 sec . 3) 40 m in 8 sec . 4) 80 m in 4 sec .

Hint: The distance travelled by the car is area under the curve. $(s=\frac{1}{2} \times 8 \times 20=80 m)$

36). A body is dropped from a certain height h . The speed-time graph from the time it is dropped, till it reaches its original position is

1)

2)

3)

4)

37). The velocity-time graph of a body is as shown in figure below. The displacement of body from $(t=2 s)$ to $(t=7 s)$ is

1) 45 m 2) 35 m 3) 50 m 4) 55 m

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

38). 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: $$\frac{v_A}{v_B}=\frac{\tan \theta_1}{\tan \theta_2}=\frac{\tan 60}{\tan 30}=\frac{\sqrt{3}}{1 / \sqrt{3}}=3$$