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Kinematics-1D

538 Questions Start Allen Test
All Exams Allen Advance Errorless
2014 Q51 Advance ARCHIVE: JEE MAIN MCQ
From a tower of height $H$ , a particle is thrown vertically upwards with a speed $u$ . The time taken by the particle, to hit the ground, is $n$ times that taken by it to reach the highest point of its path. The relation between $H$ , $u$ and $n$ is
A.
$gH = (n - 2)u^2$
B.
$2gH = n^2 u^2$
C.
$gH = (n - 2)^2 u^2$
D.
$2gH = nu^2 (n - 2)$
JEE (Advanced) 2014 Q52 Advance ARCHIVE: JEE ADVANCED Numerical
A rocket is moving in a gravity free space with a constant acceleration of $2\mathrm{ms}^{-2}$ along $+x$ direction (shown in figure). The length of a chamber inside the rocket is $4\mathrm{m}$ . A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3\mathrm{ms}^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2\mathrm{ms}^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each.
JEE (Advanced) 2014 Q53 Advance ARCHIVE: JEE ADVANCED Numerical
Airplanes A and B are flying with constant velocity in the same vertical plane at angles $30^{\circ}$ and $60^{\circ}$ with respect to the horizontal respectively as shown in figure. The speed of A is $100\sqrt{3}$ ms $^{-1}$ . At time t=0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at $t=t_{0}$ , A just escapes being hit by B, $t_{0}$ in seconds is
JEE-Main 2013 Q54 Allen JEE-Main PYQs MCQ
A projectile is given an initial velocity of $(\hat{t} + 2\hat{j})$ m/s, where $\hat{t}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10 \, m/s^{2}$ , the equation of its trajectory is :
A.
$y = x - 5x^{2}$
B.
$y = 2x - 5x^{2}$
C.
$4y = 2x - 5x^{2}$
D.
$4y = 2x - 25x^{2}$
2011 Q55 Advance ARCHIVE: JEE MAIN MCQ
An object moving with a speed of $6.25 \, ms^{-1}$ , is decelerated at a rate given by $\frac{dv}{dt} = -2.5\sqrt{v}$ , where v is the instantaneous speed. The time taken by the object, to come to rest, would be
A.
1 s
B.
2 s
C.
4 s
D.
8 s
2010 Q56 Advance ARCHIVE: JEE MAIN MCQ
A particle is moving with velocity $\vec{v} = K(y\hat{i} + x\hat{j})$ where $K$ is a constant. The general equation for its path is
A.
$y^{2} = x^{2} + \text{constant}$
B.
$y = x^{2} + \text{constant}$
C.
$y^{2} = x + \text{constant}$
D.
$xy = \text{constant}$
2009 Q57 Advance ARCHIVE: JEE MAIN MCQ
A particle has an initial velocity $3\hat{i} + 4\hat{j}$ and an acceleration of $0.4\hat{i} + 0.3\hat{j}$ . Its speed after 10 s is
A.
10 units
B.
$7\sqrt{2}$ units
C.
7 units
D.
8.5 units
JEE (Advanced) 2008 Q58 Advance ARCHIVE: JEE ADVANCED MCQ
Statement-I: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary. Statement-II: If the observer and the object are moving at velocities $v_{1}$ and $v_{2}$ , respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $v_{2} - v_{1}$ .
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
IIT-JEE 2005 Q59 Advance ARCHIVE: JEE ADVANCED MCQ
The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement?
A.
B.
C.
D.
IIT-JEE 2004 Q60 Advance ARCHIVE: JEE ADVANCED MCQ
A small block slides without friction down an inclined plane starting from rest. Let $S_{n}$ be the distance travelled from time $t = n - 1$ to $t = n$ . Then $\frac{S_n}{S_{n+1}}$ is
A.
$\frac{2n - 1}{2n}$
B.
$\frac{2n + 1}{2n - 1}$
C.
$\frac{2n - 1}{2n + 1}$
D.
$\frac{2n}{2n + 1}$
IIT-JEE 2004 Q61 Advance ARCHIVE: JEE ADVANCED MCQ
A particle starts from rest. Its acceleration $(a)$ versus time $(t)$ is as shown in the figure. The maximum speed of the particle will be
A.
$110\mathrm{ms}^{-1}$
B.
$55\mathrm{ms}^{-1}$
C.
$550\mathrm{ms}^{-1}$
D.
$660\mathrm{ms}^{-1}$
CBSE PMT 2003 Basic Level Q62 Errorless Motion Under Gravity MCQ
The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B
A.
18m
B.
6m
C.
$\frac{2}{3}m$
D.
$\frac{2}{9}m$
CPMT 2003 Basic Level Q63 Errorless Motion Under Gravity MCQ
Two balls are dropped from heights h and 2h respectively from the earth surface. The ratio of time of these balls to reach the earth is
A.
$1 : \sqrt{2}$
B.
$\sqrt{2} : 1$
C.
2 : 1
D.
1 : 4
MP PET 2002 Basic Level Q64 Errorless Speed and Velocity MCQ
The ratio of the numerical values of the average velocity and average speed of a body is always
A.
Unity
B.
Unity or less
C.
Unity or more
D.
Less than unity
MP PMT 2002 Basic Level Q65 Errorless Motion Under Gravity MCQ
A body falling from a high Minaret travels 40 meters in the last 2 seconds of its fall to ground. Height of Minaret in meters is (take $g = 10m / s^2$ )
A.
60
B.
45
C.
80
D.
50
Kerala PMT 2002 Basic Level Q66 Errorless Motion Under Gravity MCQ
A cricket ball is thrown up with a speed of $19.6 \, ms^{-1}$ . The maximum height it can reach is
A.
9.8 m
B.
19.6 m
C.
29.4 m
D.
39.2 m
AIIMS 2002 Basic Level Q67 Errorless Motion Under Gravity MCQ
Three different objects of masses $m_1, m_2$ and $m_3$ are allowed to fall from rest and from the same point 'O' along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of
A.
$m_1: m_2: m_3$
B.
$m_1: 2m_2: 3m_3$
C.
$1: 1: 1$
D.
$\frac{1}{m_1}: \frac{1}{m_2}: \frac{1}{m_3}$
Kerala (Engg.) 2001 Basic Level Q68 Errorless Speed and Velocity MCQ
A particle moves along a semicircle of radius 10m in 5 seconds. The velocity of the particle is
A.
$2\pi ms^{-1}$
B.
$4\pi ms^{-1}$
C.
$2 ms^{-1}$
D.
$4 ms^{-1}$
CBSE PMT 2001 Basic Level Q69 Errorless Speed and Velocity MCQ
A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of length 850 meters is
A.
56 sec
B.
68 sec
C.
80 sec
D.
92 sec
MP PMT 2001 Basic Level Q70 Errorless Acceleration MCQ
A particle moves along a straight line such that its displacement at any time t is given by $s = t^{3} - 3t^{2} + 2$ meter. The displacement when the acceleration becomes zero is
A.
0 meter
B.
2 meter
C.
3 meter
D.
- 2 meter
DCE 2001; AIIMS 2002 Advance Level Q71 Errorless Velocity Time Graph MCQ
A particle starts from rest, accelerates at $2 \, m/s^{2}$ for 10s and then goes for constant speed for 30s and then decelerates at $4 \, m/s^{2}$ till it stops. What is the distance travelled by it
A.
750 m
B.
800 m
C.
700 m
D.
850 m
UPSEAT 2001 Basic Level Q72 Errorless Motion Under Gravity MCQ
A particle when thrown, moves such that it passes from same height at 2 and 10s, the height is
A.
g
B.
2g
C.
5g
D.
8g
11-JEE 2000 Q73 Advance ARCHIVE: JEE ADVANCED MCQ
A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $\frac{1}{2} d$ . Neglecting subsequent motion and air resistance, its velocity $v$ varies with the height $h$ above the ground as
A.
B.
C.
D.
DCE 2000 Basic Level Q74 Errorless Distance and Displacement MCQ
A body moves 6 m north. 8 m east and 10 m vertically upwards, what is its resultant displacement from initial position
A.
$10\sqrt{2}m$
B.
10m
C.
$\frac{10}{\sqrt{2}}m$
D.
$10\times2m$
BHU 2000 Basic Level Q75 Errorless Acceleration MCQ
A body is moving according to the equation $x = at + bt^{2} - ct^{3}$ where x = displacement and a, b and c are constants. The acceleration of the body is
A.
$a + 2bt$
B.
$2b + 6ct$
C.
$2b - 6ct$
D.
$3b - 6ct^{2}$