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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q251 Allen 7. PROJECTION FROM A HEIGHT MCQ
When a particle is thrown horizontally with speed u from top of tower, the displacement of the projectile at any time t is given by:
A.
$\sqrt{u^{2}t^{2}+g^{2}t^{2}}$
B.
$\sqrt{u^{2}t^{2}+\frac{1}{4}g^{2}t^{4}}$
C.
$\sqrt{u^{2}+g^{2}t^{2}}$
D.
$\sqrt{u^{2}-g^{2}t^{2}}$
Q252 Allen 7. PROJECTION FROM A HEIGHT MCQ
A plane is flying horizontally at $98\sqrt{3}$ m/s and releases an object which reaches the ground in 10 s. The angle made by it with horizontal while hitting the ground is:
A.
$55^{\circ}$
B.
$45^{\circ}$
C.
$60^{\circ}$
D.
$30^{\circ}$
Q253 Allen 7. PROJECTION FROM A HEIGHT MCQ
From the top of a tower 78.4 m high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes an angle of $45^{\circ}$ with the horizontal, then the initial velocity of the ball is:
A.
9.8 m/s
B.
4.9 m/s
C.
19.6 m/s
D.
2.8 m/s
Q254 Allen 7. PROJECTION FROM A HEIGHT MCQ
A particle is projected horizontally with a speed of $\frac{20}{\sqrt{3}}$ m/s, from some height at t = 0. At what time will its velocity make $30^{\circ}$ angle with the initial velocity
A.
1 sec
B.
2 sec
C.
1.5 sec
D.
$2/3$ sec
Q255 Allen 7. PROJECTION FROM A HEIGHT MCQ
In the above question what will be the displacement of the particle in x-direction when its velocity makes $30^{\circ}$ angle with the initial velocity
A.
$\frac{20}{\sqrt{3}}$ m
B.
$\frac{40}{3\sqrt{3}}$ m
C.
$\frac{50}{\sqrt{3}}$ m
D.
$\frac{10}{\sqrt{3}}$ m
Q256 Allen 7. PROJECTION FROM A HEIGHT MCQ
A ball is projected upwards from the top of a tower with a velocity of 50 m/s making an angle of $30^{\circ}$ with the horizontal. The height of the tower is 70m. After how much time from the instant of throwing, will the ball reach the ground?
A.
2 s
B.
5 s
C.
7 s
D.
9 s
Q257 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Which one of the following represents the displacement-time graph of two objects A and B moving with zero relative speed :-
A.
B.
C.
D.
Q258 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A monkey is climbing up a tree at a speed of 3 m/s. A dog runs towards the tree with a speed of 4 m/s. What is the relative speed of the dog as seen by the monkey?
A.
> 7 m/s
B.
Between 5 m/s and 7 m/s
C.
5 m/s
D.
< 5 m/s
Q259 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A train is moving towards east and a car is along north, both with same speed. The observed direction of car to the passenger in the train is:-
A.
East-north direction
B.
West-north direction
C.
South-east direction
D.
None of these
Q260 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Two car A & B start from rest (from the same point) in same direction with acceleration 8 m/sĀ² & 4 m/sĀ² respectively then acceleration of car B in frame of A(Take direction of motion of car is positive) :-
A.
4 m/sĀ²
B.
-4 m/sĀ²
C.
12 m/sĀ²
D.
None of these
Q261 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A motorcycle is moving with a velocity of 80 km/h and a car is moving with a velocity of 65 km/h in the opposite direction. What is the relative velocity of the motorcycle with respect to the car?
A.
15 km/h
B.
20 km/h
C.
25 km/h
D.
145 km/h
Q262 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Two cars A and B start moving from the same point with same speed v = 5 km/minute. Car A moves towards south and car B is moving towards west. What is the relative velocity of B with respect to A?
A.
$5\sqrt{2}$ km/min towards South-East
B.
$5\sqrt{2}$ km/min towards North-West
C.
$5\sqrt{2}$ km/min towards South-West
D.
$5\sqrt{2}$ km/min towards North-East
Q263 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A train is moving towards East with a speed 20 m/s. A person is running on the roof of the train with a speed 3 m/s in the direction of motion of train. Velocity of the person as seen by an observer on ground will be :
A.
23 m/s towards East
B.
17 m/s towards East
C.
23 m/s towards West
D.
17 m/s towards West
Q264 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A jet air plane travelling with a speed of 500 km/h ejects its products of combustion with a speed of 1600 km/h relative to the jet plane. The speed of the latter with respect to an observer on the ground is:-
A.
1600 km/h
B.
2100 km/h
C.
1100 km/h
D.
500 km/h
Q265 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A train moves in north direction with a speed of 54 km/h. A monkey is running on the roof of the train, against its motion with a velocity of 36 km/h. with respect to train. The velocity of monkey as observed by a man standing on the ground is:
A.
5 m/s due north
B.
25 m/s due south
C.
10 m/s due south
D.
10 m/s due north
Q266 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A lift is moving upwards with acceleration a. A man in the lift drops a ball within the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively:
A.
g, g
B.
g - a, g - a
C.
g + a, g
D.
a, g
Q267 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A stone is thrown upwards and it rises to a height of 200 m. The relative velocity of the stone with respect to the earth will be minimum at:-
A.
Height of 100 m
B.
Height of 150 m
C.
Highest point
D.
The ground
Q268 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A 100 m long train crosses a man travelling at 5 km/h, in opposite direction in 6 seconds, then the velocity of train is:-
A.
40 km/h
B.
55 km/h
C.
20 km/h
D.
45 km/h
Q269 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A 300 metres long train is moving due north with a speed of 20 m/s. A small bird is flying due south a little above the train with 5 m/s speed The time taken by the bird to cross the train is :-
A.
6 s
B.
7 s
C.
9 s
D.
12 s
Q270 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Two trains each 100 m long, are travelling in opposite directions with respective velocities 35 m/s and 15 m/s. The time of crossing is:-
A.
2 s
B.
4 s
C.
$2\sqrt{3}s$
D.
$4\sqrt{3}s$
Q271 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
A train 200 m long crosses a bridge 300 m long. It enters the bridge with a speed of 30 ms $^{-1}$ and leaves it with a speed of 50 ms $^{-1}$ . What is the time taken to cross the bridge?
A.
2.5s
B.
7.5s
C.
12.5s
D.
15.0s
Q272 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Two cars get closer by 8 m in every second while travelling in the opposite directions. They get closer by 0.8 m in every second while travelling in the same direction. What are the speeds of the two cars?
A.
$4 \, ms^{-1}$ and $4.4 \, ms^{-1}$
B.
$4.4 \, ms^{-1}$ and $3.6 \, ms^{-1}$
C.
$4 \, ms^{-1}$ and $3.6 \, ms^{-1}$
D.
$4 \, ms^{-1}$ and $3 \, ms^{-1}$
Q273 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Velocity of a swimmer in still water is 5 m/s. If he takes 10 sec to swim upstream a distance of 30 m, then the speed of river is :-
A.
3 m/s
B.
5 m/s
C.
10 m/s
D.
2 m/s
Q274 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Two cars are moving in the same direction with the same speed of 60 km/h. They are separated by 10 km. What is the speed of a car moving in the opposite direction if it meets the two cars at an interval of 5 minute?
A.
45 km/h
B.
60 km/h
C.
105 km/h
D.
None
Q275 Allen 8. RELATIVE MOTION IN ONE DIMENSION MCQ
Four persons P, Q, R and S of same mass travel with same speed u along a square of side 'd' such that each one always faces the other. After what time will they meet each other?
A.
$\frac{\mathrm{d}}{\mathrm{u}}$
B.
$\frac{2\mathrm{d}}{3\mathrm{u}}$
C.
$\frac{2\mathrm{d}}{\mathrm{u}}$
D.
$\mathrm{d}\sqrt{3}\mathrm{u}$