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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q301 Allen 9. 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.
$90^{\circ}$
Q302 Allen 9. 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
Q303 Allen 10. 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
Q304 Allen 10. 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.
$\frac{11}{5}\left(\hat{i} + \hat{j}\right)$
Q305 Allen 10. 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.
$-2n\beta^{2}x^{-2n-1}$
Q306 Allen 10. 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
Q307 Allen 10. 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.
$\vec{\mathbf{r}}_1 \times \vec{\mathbf{v}}_1 = \vec{\mathbf{r}}_2 \times \vec{\mathbf{v}}_2$
Q308 Allen 10. 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.
$\frac{A}{2} + \frac{B}{3}$
Q309 Allen 10. 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.
$\frac{a+f}{2(b-1)}$
Q310 Allen 10. 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.
$\frac{t_{1}+t_{2}}{2}$
Q311 Allen 10. 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
Q312 Allen 10. 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.
30Ā° west
B.
0Ā°
C.
60Ā° west
D.
45Ā° west
Q313 Allen 10. 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.
$1:2\sqrt{3}$
Q314 Allen 10. 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.
$t_{1} = t_{2}$
Q315 Allen 10. 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
Q316 Allen 10. PYQ MCQ
A person travelling in a straight line moves with a constant velocity $v_{1}$ for certain distance 'x' and with a constant velocity $v_{2}$ for next equal distance. The average velocity v is given by the relation
A.
$\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
B.
$\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
C.
$\frac{v}{2} = \frac{v_{1} + v_{2}}{2}$
D.
$v = \sqrt{v_{1}v_{2}}$
Q317 Allen 10. PYQ MCQ
A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is: $(g = 10 \, \text{m/s}^2)$
A.
300 m
B.
360 m
C.
340 m
D.
320 m
Q318 Allen 10. PYQ MCQ
A person sitting in the ground floor of a building notices through the window, of height 1.5 m, a ball dropped from the roof of the building crosses the window in 0.1 s. What is the velocity of the ball when it is at the topmost point of the window? $(g = 10 \, \text{m/s}^2)$
A.
15.5 m/s
B.
14.5 m/s
C.
4.5 m/s
D.
20 m/s
Q319 Allen 10. PYQ MCQ
A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let $S_{n}$ be the distance travelled by the block in the interval t = n - 1 to t = n. Then, the ratio $\frac{S_{n}}{S_{n+1}}$ is:
A.
$\frac{2n-1}{2n}$
B.
$\frac{2n-1}{2n+1}$
C.
$\frac{2n+1}{2n-1}$
D.
$\frac{2n}{2n-1}$
Q320 Allen 10. PYQ MCQ
A car starts from rest and accelerates at $5 \, m/s^{2}$ . At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6 \, s$ ? (Take $g = 10 \, m/s^{2}$ )
A.
$20 \, m/s, 5 \, m/s^{2}$
B.
$20 \, m/s, 0$
C.
$20\sqrt{2} \, m/s, 0$
D.
$20\sqrt{2} \, m/s, 10 \, m/s^{2}$
Q321 Allen 10. PYQ MCQ
A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle 'Īø' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, Īø, is then given by:
A.
$\theta = \cos^{-1}\left(\frac{gT^{2}}{\pi^{2}R}\right)^{\frac{1}{2}}$
B.
$\theta = \cos^{-1}\left(\frac{\pi^{2}R}{gT^{2}}\right)^{\frac{1}{2}}$
C.
$\theta = \sin^{-1}\left(\frac{\pi^{2}R}{gT^{2}}\right)^{\frac{1}{2}}$
D.
$\theta = \sin^{-1}\left(\frac{2gT^{2}}{\pi^{2}R}\right)^{\frac{1}{2}}$
Q322 Allen 10. PYQ MCQ
The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the x-axis as shown in the figure. The ratio of their respective velocity is :
A.
$1:1$
B.
$1:2$
C.
$1:\sqrt{3}$ $
D.
\sqrt{3}:1$
Q323 Allen 10. PYQ MCQ
The ratio of the distances travelled by a freely falling body in the $1^{st}$ , $2^{nd}$ , $3^{rd}$ and $4^{th}$ second:
A.
1:4:9:16
B.
1:3:5:7
C.
1:1:1:1
D.
1:2:3:4
Q324 Allen 10. PYQ MCQ
A ball is projected with a velocity, $10 \, ms^{-1}$ , at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be:
A.
$5\sqrt{3}ms^{-1}$
B.
$5 \, ms^{-1}$
C.
$10 \, ms^{-1}$
D.
Zero
Q325 Allen 10. PYQ MCQ
A cricket ball is thrown by a player at a speed of 20 m/s in a direction $30^{\circ}$ above the horizontal. The maximum height attained by the ball during its motion is: $(g = 10 \, \text{m/s}^{2})$
A.
5 m
B.
10 m
C.
20 m
D.
25 m