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Kinematics-1D

538 Questions Start Allen Test
All Exams Allen Advance Errorless
Advance Level Q501 Errorless Equation of Kinematics (uniform Acceleration) MCQ
A body starts from rest with uniform acceleration. If its velocity after n second is $\nu$ , then its displacement in the last two seconds is
A.
$\frac{2\nu(n+1)}{n}$
B.
$\frac{\nu(n+1)}{n}$
C.
$\frac{\nu(n-1)}{n}$
D.
$\frac{2\nu(n-1)}{n}$
Advance Level Q502 Errorless Equation of Kinematics (uniform Acceleration) MCQ
Two particles move in a straight line towards each other with initial velocities $\nu_{1}$ and $\nu_{2}$ and retardation $a_{1}$ and $a_{2}$ towards each other. The maximum initial separation between the two particles so that they may meet must be
A.
$\frac{\left(\nu_{1}+\nu_{2}\right)}{2\left(a_{1}+a_{2}\right)}$
B.
$\frac{\left(\nu_{1}+\nu_{2}\right)^{2}}{2\left(a_{1}+a_{2}\right)}$
C.
$\frac{\left(\nu_{1}+\nu_{2}\right)}{2a_{1}a_{2}}$
D.
$\frac{\left(\nu_{1}+\nu_{2}\right)}{2\left(a_{1}+a_{2}\right)^{2}}$
Advance Level Q503 Errorless Equation of Kinematics (uniform Acceleration) MCQ
A point starts moving in a straight line with a certain acceleration. At a time t after beginning of motion the acceleration suddenly becomes retardation of the same value. The time in which the point returns to the initial point is
A.
$\sqrt{2t}$
B.
$(2 + \sqrt{2})t$
C.
$\frac{t}{\sqrt{2}}$
D.
Cannot be predicted unless acceleration is given
Advance Level Q504 Errorless Equation of Kinematics (uniform Acceleration) MCQ
A particle is moving in a straight line and passes through a point O with a velocity of $6 \, ms^{-1}$ . The particle moves with a constant retardation of $2 \, ms^{-2}$ for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O
A.
3s
B.
8s
C.
Never
D.
4s
Advance Level Q505 Errorless Equation of Kinematics (uniform Acceleration) MCQ
A bird flies for 4 s with a velocity of $\left| t - 2 \right| m / s$ in a straight line, where t = time it seconds. It covers a distance of
A.
2 m
B.
4 m
C.
6 m
D.
8 m
Basic Level Q506 Errorless Equation of Kinematics (variable Acceleration) MCQ
A particle, initially at rest, starts moving in a straight line with an acceleration $a = 6t + 4m/s^{2}$ . The distance covered by it in 3 s is
A.
30 m
B.
60 m
C.
45 m
D.
15 m
Basic Level Q507 Errorless Equation of Kinematics (variable Acceleration) MCQ
The Initial velocity of a particle is $u$ (at $t = 0$ ) and the acceleration $f$ is given by $a t$ . Which of the following relation is valid
A.
$v = u + a t^2$
B.
$v = u + a \frac{t^2}{2}$
C.
$v = u + a t$
D.
$v = u$
Advance Level Q508 Errorless Equation of Kinematics (variable Acceleration) MCQ
The velocity of a particle is dependent on the time as $v = k(t - 1)$ where $k = 2 \, m/s^{2}$ . the distance covered in first three seconds will be
A.
18 m
B.
5 m
C.
3 m
D.
6 m
Advance Level Q509 Errorless Equation of Kinematics (variable Acceleration) MCQ
A particle is projected with velocity $v_{0}$ along x-axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e., $a = \alpha x^{2}$ . The distance at which the particle stops is
A.
$\sqrt{\frac{3v_{0}}{2\alpha}}$
B.
$\left(\frac{3v_{o}}{2\alpha}\right)^{\frac{1}{3}}$
C.
$\sqrt{\frac{3v_{0}^{2}}{2\alpha}}$
D.
$\left(\frac{3v_{0}^{2}}{2\alpha}\right)^{\frac{1}{3}}$
Basic Level Q510 Errorless Motion Under Gravity MCQ
A ball is dropped from top of a tower of 100m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50 m/s ( $g = 10 \, m / s^{2}$ ). They will cross each other after
A.
1s
B.
2s
C.
3s
D.
4s
Basic Level Q511 Errorless Motion Under Gravity MCQ
A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initial velocity (u) of the ball and for how much time (T) it remains in the air $[g = 10m/s^{2}]$
A.
u = 10 m/s, T = 2s
B.
u = 10 m/s, T = 4s
C.
u = 20 m/s, T = 2s
D.
u = 20 m/s, T = 4s
Basic Level Q512 Errorless Motion Under Gravity MCQ
A balloon starts rising from the ground with an acceleration of $1.25 \, m/s^{2}$ after 8s, a stone is released from the balloon. The stone will ( $g = 10 \, m/s^{2}$ )
A.
Reach the ground in 4 second released
B.
Begin to move down after being
C.
Have a displacement of 50 m
D.
Cover a distance of 40 m in reaching the ground
Basic Level Q513 Errorless Motion Under Gravity MCQ
The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is $30^{\circ}$ ) is
A.
$\frac{1}{2}$ sec
B.
2 sec
C.
4 sec
D.
1 sec
Basic Level Q514 Errorless Motion Under Gravity MCQ
A ball is dropped downwards. After 1 second another ball is dropped downwards from the same point. What is the distance between them after 3 seconds
A.
25 m
B.
20 m
C.
50 m
D.
9.8 m
Basic Level Q515 Errorless Motion Under Gravity MCQ
A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of $1m$ each will then be
A.
All equal, being equal to $\sqrt{2 / g}$ second
B.
In the ratio of square roots of the integers 1, 2, 3, ....
C.
In the ratio of the difference in the square roots of the integers i.e. $\sqrt{1}, (\sqrt{2} - \sqrt{1}), (\sqrt{3} - \sqrt{2}), (\sqrt{4} - \sqrt{3})$ .....
D.
In the ratio of the reciprocal of the square roots of the integers i.e. $\frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{4}}$
Basic Level Q516 Errorless Motion Under Gravity MCQ
A rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \, m/sec^2$ . If after 5 sec its engine is switched off, the maximum height of the rocket from earth's surface would be
A.
245 m
B.
490 m
C.
980 m
D.
735 m
Basic Level Q517 Errorless Motion Under Gravity MCQ
A body is slipping from an inclined plane of height h and length l. If the angle of inclination is $\theta$ , the time taken by the body to come from the top to the bottom of this inclined plane is
A.
$\sqrt{\frac{2h}{g}}$
B.
$\sqrt{\frac{2l}{g}}$
C.
$\frac{1}{\sin\theta}\sqrt{\frac{2h}{g}}$
D.
$\sin\theta\sqrt{\frac{2h}{g}}$
Basic Level Q518 Errorless Motion Under Gravity MCQ
A frictionless wire AB is fixed on a sphere of radius R. A very small spherical ball slips on this wire. The time taken by this ball to slip from A to B is
A.
$\frac{2\sqrt{gR}}{g\cos\theta}$
B.
$2\sqrt{gR}\cdot\frac{\cos\theta}{g}$
C.
$2\sqrt{\frac{R}{g}}$
D.
$\frac{gR}{\sqrt{g\cos\theta}}$
Basic Level Q519 Errorless Motion Under Gravity MCQ
Two particles one 0.98 m vertically above the other are released simultaneously. They fall under gravity $(g = 9.8 \, m/s^{2})$ . The separation between the two particles after 2 s will be
A.
0.49 m
B.
4.9 m
C.
0.98 m
D.
19.6 m
Basic Level Q520 Errorless Motion Under Gravity MCQ
Two balls are dropped from different heights. One ball is dropped 2 sec after the other ball. If both balls reach the ground simultaneously after 5 sec of dropping the first ball the difference of initial heights of the two balls will be $(g = 9.8 \, m/s^{2})$
A.
58.8 v
B.
78.4 m
C.
98 m
D.
117.6 m
Basic Level Q521 Errorless Motion Under Gravity MCQ
A balloon is moving upwards with a constant velocity of 5 m/s. A stone is dropped from it. If at the moment of dropping the stone the balloon is at height of 50 m, then when the stone will hit the ground, at that time the height of the balloon will be $(g = 10 \, m / s^{2})$
A.
68.3 m
B.
63.5 m
C.
75.5 m
D.
88.7 m
Basic Level Q522 Errorless Motion Under Gravity MCQ
A stone thrown upwards with a velocity u reaches up to a height h. If the initial velocity is 2u the height attained would be
A.
2h
B.
4h
C.
8h
D.
16h
Basic Level Q523 Errorless Motion Under Gravity MCQ
A person throws balls into the air one after the other at an interval of one second. The next ball is thrown when the velocity of the ball thrown earlier is zero. To what height the ball rise (Take $g = 10 \, m / s^{-2}$ )
A.
5 m
B.
10 m
C.
25 m
D.
40 m
Basic Level Q524 Errorless Motion Under Gravity MCQ
A body is projected vertically up with a velocity v and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are
A.
$\vec{v}/2$ and v/2
B.
o and v/2
C.
o and o
D.
$\vec{v}/2$ and o
Basic Level Q525 Errorless Motion Under Gravity MCQ
Two balls A and B are simultaneously thrown. A is thrown from ground level with a velocity of $20 \, ms^{-1}$ in the upward direction and B is thrown from a height of 40 m in the downward direction with same velocity. Where will the two balls meet
A.
15 m
B.
25 m
C.
35 m
D.
45 m