← Back to Physics-I

Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q551 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
Rain is falling vertically with a speed of 3 m/s. If a man is running with the same speed then the velocity of rain w.r.t. man is :-
A.
3 m/s
B.
6 m/s
C.
4.2 m/s
D.
0 m/s
Q552 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A man is walking on a road with a velocity of 5km/h. When suddenly it starts raining, velocity of rain is 10km/h in vertically downward direction, relative velocity of the rain with respect to man is:
A.
$\sqrt{13}$ km/hr
B.
$\sqrt{7}$ km/hr
C.
$\sqrt{109}$ km/hr
D.
$5\sqrt{5}$ km/hr
Q553 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
If the rain is falling vertically downwards with velocity 20 m/s and if a bike is going with velocity 30 m/s. Calculate at what angle from the vertical a man on the bike must incline his umbrella so that he can save himself from rain:
A.
$\tan^{-1}\left(\frac{2}{3}\right)$
B.
$\tan^{-1}\left(\frac{3}{2}\right)$
C.
$\tan^{-1}(1)$
D.
$\tan^{-1}\left(\frac{6}{5}\right)$
Q554 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
If rain is falling at some angle from vertical and has horizontal velocity 2 m/s in east direction. With what velocity a man must move on the horizontal surface so that rain will appear vertical to him :-
A.
4 m/s in east direction
B.
2 m/s in east direction
C.
2 m/s in west direction
D.
2 m/s in a circular path
Q555 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A boy is running on a levelled road with velocity (u) with a long hollow tube in his hand. Water is falling vertically downwards with velocity (v). At what angle to the vertical, should he incline the tube so that the water drops enters without touching its side:
A.
$\tan^{-1}\left(\frac{v}{u}\right)$
B.
$\sin^{-1}\left(\frac{v}{u}\right)$
C.
$\tan^{-1}\left(\frac{u}{v}\right)$
D.
$\cos^{-1}\left(\frac{v}{u}\right)$
Q556 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A river is flowing at the rate of 8 km/h. A swimmer swims across the river with a velocity of 10 km/h w.r.t. water. The resultant velocity of the man will be in (km/h):-
A.
$\sqrt{117}$
B.
$\sqrt{340}$
C.
$\sqrt{164}$
D.
$3\sqrt{40}$
Q557 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A river is flowing from W to E with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the north :-
A.
$30^{\circ}$ with downstream
B.
$60^{\circ}$ with downstream
C.
$120^{\circ}$ with downstream
D.
South
Q558 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A river 4.0 miles wide is flowing at the rate of 2 miles/hr. The minimum time taken by a boat to cross the river with a speed v = 2 miles/hr (in still water) is approximately
A.
1 hr and 0 minute
B.
2 hr
C.
1 hr and 12 minutes
D.
2 hr and 25 minutes
Q559 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A river flows from east to west with a speed of 5m/min. A man on south bank of river, capable of swimming at the rate of 10 m/min in still water, wants to swim across the river in shortest time; he should swim :
A.
due north
B.
due north-east
C.
due north-east with double the speed of river
D.
none of the above
Q560 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A boat-man can row a boat to make it move with a speed of 10 km/h in still water. River flows steadily at the rate of 6 km/h. and the width of the river is 4 km. If the boat man cross the river along the minimum distance of approach then time elapsed in rowing the boat will be:
A.
$\frac{2\sqrt{3}}{5}$ h
B.
$\frac{2}{5\sqrt{3}}$ h
C.
$\frac{3\sqrt{2}}{5}$ h
D.
$\frac{1}{2}$ h
Q561 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
A man wishes to swim across a river 0.5 km wide. If he can swim at the rate of $\sqrt{2}$ km/h in still water and the river flows at the rate of 1 km/h. The angle made by the direction (w.r.t. the flow of the river) along which he should swim so as to reach a point exactly opposite his starting point, should be :
A.
$60^{\circ}$
B.
$120^{\circ}$
C.
$135^{\circ}$
D.
$90^{\circ}$
Q562 Allen RELATIVE MOTION IN TWO DIMENSION MCQ
Two particles are separated by a horizontal distance x as shown in figure. They are projected as shown in figure with different initial speeds. The time after which the horizontal distance between them becomes zero is :
A.
$\frac{\mathbf{x}}{\mathbf{u}}$
B.
$\frac{\mathrm{u}}{2\mathrm{x}}$
C.
$\frac{\mathrm{x}}{2\mathrm{u}}$
D.
none of these
Q563 Allen PYQ MCQ
A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m/s $^{2}$ ) is: (given g = 9.8 m/s $^{2}$ )
A.
3.5
B.
5.9
C.
16.3
D.
110.8
Q564 Allen PYQ MCQ
A particle is moving such that its position coordinates (x, y) are (2m, 3m) at time t = 0 (6m, 7m) at time t = 2 s and (13m, 14m) at time t = 5s. Average velocity vector ( $\vec{V}_{av}$ ) from t = 0 to t = 5 s is
A.
$\frac{1}{5}\left(13\hat{i} + 14\hat{j}\right)$
B.
$\frac{7}{3}\left(\hat{i} + \hat{j}\right)$
C.
$2\left(\hat{i} + \hat{j}\right)$
D.
$\frac{11}{5}\left(\hat{i} + \hat{j}\right)$
Q565 Allen PYQ MCQ
A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $v(x) = \beta x^{-2n}$ 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:
A.
$-2n\beta^{2}x^{-4n-1}$
B.
$-2\beta^{2}x^{-2n+1}$
C.
$-2n\beta^{2}e^{-4n+1}$
D.
$-2n\beta^{2}x^{-2n-1}$
Q566 Allen PYQ MCQ
A ship A is moving Westwards with a speed of 10 km/h and a ship B 100 km South of A, is moving Northwards with a speed of 10 km/h. The time after which the distance between them becomes shortest, is :-
A.
5 h
B.
$5\sqrt{2}$ h
C.
$10\sqrt{2}$ h
D.
0 h
Q567 Allen PYQ MCQ
Two particles A and B, move with constant velocities $\vec{\mathbf{v}}_1$ and $\vec{\mathbf{v}}_2$ . At the initial moment their position vectors are $\vec{\mathbf{r}}_1$ and $\vec{\mathbf{r}}_2$ respectively. The condition for particle A and B for their collision is:-
A.
$\vec{\mathbf{r}}_1 - \vec{\mathbf{r}}_2 = \vec{\mathbf{v}}_1 - \vec{\mathbf{v}}_2$
B.
$\frac{\vec{\mathbf{r}}_1 - \vec{\mathbf{r}}_2}{|\vec{\mathbf{r}}_1 - \vec{\mathbf{r}}_2|} = \frac{\vec{\mathbf{v}}_2 - \vec{\mathbf{v}}_1}{|\vec{\mathbf{v}}_2 - \vec{\mathbf{v}}_1|}$
C.
$\vec{\mathbf{r}}_1 \cdot \vec{\mathbf{v}}_1 = \vec{\mathbf{r}}_2 \cdot \vec{\mathbf{v}}_2$
D.
$\vec{\mathbf{r}}_1 \times \vec{\mathbf{v}}_1 = \vec{\mathbf{r}}_2 \times \vec{\mathbf{v}}_2$
Q568 Allen PYQ MCQ
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:
A.
$\frac{3}{2}A + 4B$
B.
$3A + 7B$
C.
$\frac{3}{2}A + \frac{7}{3}B$
D.
$\frac{A}{2} + \frac{B}{3}$
Q569 Allen PYQ MCQ
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?
A.
$\frac{a+f}{2(1+b)}$
B.
$\frac{f-a}{2(1+b)}$
C.
$\frac{a-f}{1+b}$
D.
$\frac{a+f}{2(b-1)}$
Q570 Allen PYQ MCQ
Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_{1}$ . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_{2}$ . The time taken by her to walk up on the moving escalator will be
A.
$\frac{t_{1}t_{2}}{t_{2}-t_{1}}$
B.
$\frac{t_{1}t_{2}}{t_{2}+t_{1}}$
C.
$t_{1}-t_{2}$
D.
$\frac{t_{1}+t_{2}}{2}$
Q571 Allen PYQ MCQ
The x and y coordinates of the particle at any time are $x = 5t - 2t^{2}$ and y = 10t respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is:
A.
$5 \, m/s^{2}$
B.
$-4 \, m/s^{2}$
C.
$-8 \, m/s^{2}$
D.
0
Q572 Allen PYQ MCQ
The speed of a swimmer in still water is 20 m/s. The speed of river water is 10 m/s and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes w.r.t. north is given by:
A.
30° west
B.
0°
C.
60° west
D.
45° west
Q573 Allen PYQ MCQ
When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal, it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object the shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}:x_{2}$ will be
A.
$1:\sqrt{2}$
B.
$\sqrt{2}:1$
C.
$1:\sqrt{3}$
D.
$1:2\sqrt{3}$
Q574 Allen PYQ MCQ
A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_{1}$ if the elevator is at rest and in time $t_{2}$ if the elevator is moving uniformly. Then:
A.
$t_{1} < t_{2}$ or $t_{1} > t_{2}$ depending upon whether the lift is going up or down
B.
$t_{1} < t_{2}$
C.
$t_{1} > t_{2}$
D.
$t_{1} = t_{2}$
Q575 Allen PYQ MCQ
Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200m with the same velocity of 25 m/s. When and where will the two bullets collide. (g = 10 m/s $^{2}$ )
A.
after 2s at a height 180 m
B.
after 2s at a height of 20 m
C.
after 4s at a height of 120 m
D.
they will not collide