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A motor car covers $1/3^{\mathrm{rd}}$ part of total distance with ${\mathrm{v}}_1$= 10 km/hr, second $1/3^{\mathrm{rd}}$ part with ${\mathrm{v}}_2$= 20 km/hr and rest $1/3^{\mathrm{rd}}$ part with ${\mathrm{v}}_3$ = 60 km/hr. What is the average speed of the car?
1. 18 km/hr
2. 45 km/hr
3. 6 km/hr
4. 22.5 km/hr

The adjoining curve represents the velocity-time graph of a particle, its acceleration values along with OA, AB, and BC in $metre/se{c}^2$ are respectively-

1.  1, 0, -0.5
2.  1, 0, 0.5
3.  1, 1, 0.5
4.  1, 0.5, 0

A ball is dropped from a certain height on a glass floor so that it rebounds elastically to the same height. If the process continues, the velocity-time graph for such a motion would be -

(i)	(ii)
(iii)	(iv)

   

1.  (i)
2.  (ii)
3.  (iii)
4.  (iv)

A particle, after starting from rest, experiences constant acceleration. If it covers a distance of ${\mathrm{S}}_1$ in the first 10 seconds and distance ${\mathrm{S}}_2$ in the next 10 sec, then-
1. ${\mathrm{S}}_2={\mathrm{S}}_1/2$
2. ${\mathrm{S}}_1$ = ${\mathrm{S}}_2$
3. ${\mathrm{S}}_1$ = 2${\mathrm{S}}_2$
4. 3${\mathrm{S}}_1$ = ${\mathrm{S}}_2$

A particle moves with constant speed v along a regular hexagon ABCDEF in the same order (i.e. A to B, B, to C, C to D, D to E, E to F, F to A....). Then the magnitude of average velocity for its motion from A to C is -
1. v
2. v/2
3. $\sqrt{3}$ v/2
4. None of these

A person is moving in a circle of radius $$r with constant speed v. The change in velocity in moving from $$A to $$B is-
       
1. \(2 v~ cos ~40^\circ\)
2. \(2 v~ sin ~40^\circ\)
3. \(2 v~ cos ~20^\circ\)
4. \(2 v~ sin ~40^\circ\)

A train accelerates from rest at a constant rate$$$\alpha$ for distance $x_1$​ and time $t_1$​. After that retards rest at to constant rate β for distance $x_2$​ in time $t_2$​ and comes to the rest, which of the following relation is correct -
(1) $$$\frac{x_1}{x_2}=\frac{\alpha }{\beta }=\frac{t_1}{t_2}$
(2) $$$\frac{x_1}{x_2}=\frac{\beta }{\alpha }=\frac{t_1}{t_2}$
(3) $$$\frac{x_1}{x_2}=\frac{\alpha }{\beta }=\frac{t_2}{t_1}$
(4) $$$\frac{x_1}{x_2}=\frac{\beta }{\alpha }=\frac{t_2}{t_1}$​​

A disc in which several grooves are cut along the chord drawn from a point 'A', is arranged in a vertical plane, several particles start slipping from 'A' along the grooves simultaneously. Assuming friction and resistance negligible, the time taken in reaching the edge of disc will be-
 

A stone is dropped into a well in which the level of water is h below the top of the well. If v is velocity of sound, the time T after which the splash is heard is given by -
(1) $$T = $\frac{2h}{v}$​
(2) $$T = $\sqrt{\frac{2h}{g}}+\frac{h}{v}$​
(3) $$T = $\sqrt{\frac{2h}{v}}+\frac{h}{g}$​
(4) $$T = $\sqrt{\frac{h}{2g}}+\frac{2h}{v}$

A body is dropped from the top of a tower covers $\frac{7}{16}$ of total height in the last second of its fall. The time of fall is -
1.  2 s
2.  4 s
3.  < 1 s
4.  > 5 s 

A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of hte distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is-
1.  4.0 m/s
2.  5.0 m/s
3.  5.5 m/s
4.  4.8 m/s 

The deceleration experienced by a moving motor boat, after its engine is cut off is given by $\frac{dv}{dt}=-k{v}^3$, where k is constant. If $v_0$​ is the magnitude of the velocity at cut off, the magnitude of the velocity at a time t after the cut-off is-
(1) $$$\frac{v_0}{2}$
(2) $$$v_0$
(3) $$$v_0$​$e^{-k/1}$
(4)$\frac{v_0}{\sqrt{\left(2v_0^{2}kt+1\right)}}$

The displacement of a particle is given by $y = a + bt + c{t}^2 - d{t}^4$. The initial velocity and acceleration are respectively-
1.  b, -4d
2.  -b, 2c
3.  b, 2c
4.  2c, -4d 

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-
                   .
      OA      ​ AB     ​ BC      ​ CD ​
(1)  +          0        +         +
(2)  −          ​0        ​0          + ​
(3)  +          0        −         0 
(4)  −          0        −         0

A particle moves along a straight line OX. At a time t(in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t - $t^3$. How long would the particle travel before coming to rest-
1.  24 m
2.  40 m
3.  56 m
4.  16 m 

A particle is moving along x-axis has acceleration f, at time t, given by $f = f_0\left(1-\frac{t}{T}\right)$, where $f_0$and T are constants. The particle at t = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the particle velocity $\left(v_x\right)$ is-
1.  $\frac{1}{2}{f}_{0}T$
2.  $f_{0}T$
3.  $\frac{1}{2}{f}_0{T}^2$
4.  $f_0{T}^2$

A bus is moving with a speed of 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus-
1.  10 m/s
2.  20 m/s
3.  40 m/s
4.  25 m/s

The motion of a particle along a straight line is described by an equation $\mathrm{x} = 8 + 12\mathrm{t}- {\mathrm{t}}^3$ where x is in metre and t is in second. The retardation of the particle when its velocity becomes zero is:
1.  6 ${\mathrm{ms}}^{-2}$
2.  12 ${\mathrm{ms}}^{-2}$
3.  24 ${\mathrm{ms}}^{-2}$
4.  zero 

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v\left(x\right)=\beta x^{-2n,}$ where $\beta$ and n are constants and x is the position of the particle. The acceleration of the particle as a function of x, is given by:
1.  $-2n{\beta }^2 x^{-2-1}$
2.  $-2n{\beta }^2 x^{-4n-1}$
3.  $-2n{\beta }^2 x^{-2n+1}$
4.  $-2n{\beta }^2 e^{-4n+1}$

If the velocity of a particle is v=At+Bt${}^2$, where A and B are constants, then the distance travelled by it between 1s and 2s is :
(1) 3A+7B
(2) $\frac{3}{2}A+\frac{7}{3}B$
(3) $\frac{A}{2}+\frac{B}{3}$
(4) $\frac{3}{2}A+4B$

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_P$​(t)=at+bt${}^2$ and $$$x_Q$​(t)= ft− $t^2$. At what time do the cars have the same velocity ?