SCRA 1998; DCE 2000; AIIMS 2003; Odisha PMT 2004
Q226
Errorless
Graphical Questions
MCQ
An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement (s) - velocity (v) graph of this object is
A.
B.
C.
D.
CBSE PMT 1997; BHU 1999; DPMT 2000; KCET 2000; JIPMER 2001, 02; AMU (Engg.) 2009; WB-JEE 2013
Q227
Errorless
Non-uniform Motion
MCQ
A particle moves along a straight line such that its displacement at any time t is given by $S = t^{3} - 6t^{2} + 3t + 4$ metres
The velocity when the acceleration is zero is
A.
$3ms^{-1}$
B.
$-12ms^{-1}$
C.
$42ms^{-1}$
D.
$-9ms^{-1}$
CPMT 1997; BHU 1998; DPMT 1999; RPET 1999; MH CET 2003
Q228
Errorless
Motion Under Gravity
MCQ
A stone dropped from the top of the tower touches the ground in 4 sec. The height of the tower is about
A.
80 m
B.
40 m
C.
20 m
D.
160 m
MP PET 1997; RPET 2001; BHU 2003; RPMT 2004, 06; Kerala PET 2009, 12; AMU (Med.) 2010
Q229
Errorless
Motion Under Gravity
MCQ
A body starts to fall freely under gravity. The distances covered by it in first, second and third second are in ratio
A.
1:3:5
B.
1:2:3
C.
1:4:9
D.
1:5:6
CPMT 1997; AIIMS 2000; MH CET 2000; CBSE PMT 2002; MP PET 2003
Q230
Errorless
Motion Under Gravity
MCQ
With what velocity a ball be projected vertically so that the distance covered by it in $5^{\text{th}}$ second is twice the distance it covers in its $6^{\text{th}}$ second ( $g = 10\,m/s^{2}$ )
A.
58.8 m/s
B.
49 m/s
C.
65 m/s
D.
19.6 m/s
RPET 1996, 99; BHU 2002; MP PET 2009
Q231
Errorless
Uniform Motion
MCQ
A person travels along a straight road for the first half time with a velocity $v_{1}$ and the next half time with a velocity $v_{2}$ . The mean velocity V of the man is
A.
$\frac{2}{V} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
B.
$V = \frac{v_{1} + v_{2}}{2}$
C.
$V = \sqrt{v_{1}v_{2}}$
D.
$V = \sqrt{\frac{v_{1}}{v_{2}}}$
MP PET 1996: CPMT 1999. 2003;
Pb. PET 2004; J & K CET 2005;
RPMT 2006; WBāJEE 2008; AMU (Engg.) 2012
Q232
Errorless
Non-uniform Motion
MCQ
The displacement of a particle is given by $y=a+bt+ct^2-dt^4$. The initial velocity and acceleration are respectively
A.
$b,-4d$
B.
$-b,2c$
C.
$b,2c$
D.
$2c,-4d$
CPMT 1996; BHU 1998; CPMT 1999; JIPMER 2000; AMU (Med.) 2001; RPET 2001, 05; Kerala PET 2002; Kerala PMT 2008
Q233
Errorless
Relative Motion
MCQ
Two trains, each 50 m long are travelling in opposite direction with velocity 10 m/s and 15 m/s. The time of crossing is
A.
2s
B.
4s
C.
$2\sqrt{3}s$
D.
$4\sqrt{3}s$
Kurukshetra CEE 1996; Kerala PMT 2006
Q234
Errorless
Critical Thinking
MCQ
A particle is dropped vertically from rest from a height. The time taken by it to fall through successive distances of 1 m each will then be
A.
All equal, being equal to $\sqrt{2 / g}$ second
B.
In the ratio of the 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. $\frac{1}{\sqrt{1}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{4}}$
Kurukshetra CEE 1996; DCE 2006
Q235
Errorless
Graphical Questions
MCQ
Figures (i) and (ii) below show the displacement-time graphs of two particles moving along the x-axis. We can say that
A.
Both the particles are having a uniformly accelerated motion
B.
Both the particles are having a uniformly retarded motion
C.
Particle (i) is having a uniformly accelerated motion while particle (ii) is having a uniformly retarded motion
D.
Particle (i) is having a uniformly retarded motion while particle (ii) is having a uniformly accelerated motion
Manipal MEE 1995; AFMC 1998;
MP PMT 1999; CPMT 2002; Kerala PMT 2005, 10
Q236
Errorless
Uniform Motion
MCQ
A car travels half the distance with constant velocity of 40 kmph and the remaining half with a constant velocity of 60 kmph. The average velocity of the car in kmph is
A.
40
B.
45
C.
48
D.
50
NTSE 1995; DCE 2006
Q237
Errorless
Non-uniform Motion
MCQ
For a moving body at any instant of time
A.
If the body is not moving, the acceleration is necessarily zero
B.
If the body is slowing, the retardation is negative
C.
If the body is slowing, the distance is negative
D.
If displacement, velocity and acceleration at that instant are known, we can find the displacement at any given time in future
CBSE PMT 1995; MP PMT 2004
Q238
Errorless
Motion Under Gravity
MCQ
A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time t/2 sec
A.
At h/2 from the ground
B.
At h/4 from the ground
C.
Depends upon mass and volume of the body
D.
At 3h/4 from the ground
EAMCET (Med.) 1995; AIIMS 1999; Pb. PMT 2004; BHU 2004
Q239
Errorless
Graphical Questions
MCQ
Velocity-time curve for a body projected vertically upwards is
A.
Parabola
B.
Ellipse
C.
Hyperbola
D.
Straight line
IIT-JEE 1993
Q240
Advance
ARCHIVE: JEE ADVANCED
MCQ
A particle P is sliding down a frictionless hemispherical bowl. It passes the point A at t=0. At this instant of time, the horizontal component of its velocity is v. A bead Q of same mass as P is ejected from A at t=0 along the horizontal string AB, with a speed v. Friction between the bead and the string may be neglected. Let $t_{P}$ and $t_{Q}$ be the respective times taken by P and Q to reach the point B, then
A.
$t_{P} < t_{Q}$
B.
$t_{P}=t_{Q}$
C.
$t_{P} > t_{Q}$
D.
$\frac{t_{\mathrm{P}}}{t_{\mathrm{Q}}} = \frac{\text{length of arc } ACB}{\text{length of chord } AB}$
IIT-JEE 1993
Q241
Advance
ARCHIVE: JEE ADVANCED
MSQ
A particle of mass m moves on the x-axis as follows: it starts from rest at t=0 from the point x=0 and comes to rest at t=1 at the point x=1. No other information is available about its motion at intermediate time $\text{(0t1)}$
. If $\alpha$ denotes the instantaneous acceleration of the particle, then
A.
$\alpha$ cannot remain positive for all $t$ in the interval $0 \leq t \leq 1$
B.
$|\alpha|$ cannot exceed 2 at any point in its path
C.
$|\alpha|$ must be $\geq 4$ at some point or points in its path
D.
$\alpha$ must change sign during the motion but no other assertion can be made with the information given
IIT-JEE 1988
Q242
Advance
ARCHIVE: JEE ADVANCED
MCQ
A boat which has a speed of $5\mathrm{kmh}^{-1}$ in still water crosses a river of width $1\mathrm{km}$ along the shortest possible path in 15 minute. The velocity of the river water in $\mathrm{kmh}^{-1}$ is
A.
1
B.
3
C.
4
D.
$\sqrt{41}$
IIT-JEE 1983
Q243
Advance
ARCHIVE: JEE ADVANCED
MCQ
A river is flowing from west to east at a speed of 5 m per minute. A man on the south bank of the river, capable of swimming at 10 m per minute in still water wants to swim across the river to a point directly opposite in the shortest time. He should then swim in a direction
A.
$6 0^{\circ}$ west of north
B.
$30^{\circ}$ east of north
C.
$30^{\circ}$ west of north
D.
$60^{\circ}$ east of north
IIT-JEE 1982
Q244
Advance
ARCHIVE: JEE ADVANCED
MCQ
In the arrangement shown in the figure, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed
A.
$2U\cos \theta$
B.
$\frac{U}{\cos\theta}$
C.
$\frac{2U}{\cos\theta}$
D.
$U \cos \theta$
IIT-JEE 1982
Q245
Advance
ARCHIVE: JEE ADVANCED
MCQ
A particle is moving Eastwards with a velocity of $5 \, ms^{-1}$ . In 10 s, the velocity changes to $5 \, ms^{-1}$ Northwards. The average acceleration in this time is
A.
zero
B.
$\frac{1}{\sqrt{2}} \, ms^{-2}$ towards North-East
C.
$\frac{1}{\sqrt{2}} \, ms^{-2}$ towards North-West
D.
$\frac{1}{2} \, ms^{-2}$ towards North
Q246
Allen
JEE-Main Pattern
MCQ
Find ratio of average speed and magnitude of average velocity of tip of minute hand in 20 minutes:
A.
$\frac{2\pi}{3\sqrt{3}}$
B.
$\frac{2\pi}{3}$
C.
$\frac{3\sqrt{3}}{2\pi}$
D.
None
Q247
Allen
JEE-Main Pattern
MCQ
The motion of a particle is defined by the position vector $\vec{r} = A(\cos t + t\sin t)\hat{\imath} +A(\sin t - t\cos t)\hat{j}$
Where t is expressed in seconds. Determine the value of t for which positions vectors and acceleration vector are perpendicular.
A.
0
B.
1
C.
3
D.
5
Q248
Allen
JEE-Main Pattern
MCQ
Now the particle is moving only along the z-axis, and its position is given by, $(t^{2}-2t-3)\hat{k}$ . At what time does the particle stand still?
A.
1
B.
3
C.
5
D.
7
Q249
Allen
JEE-Main Pattern
MCQ
A particle is moving towards East with velocity $8 \, ms^{-1}$ and acceleration $4 \, ms^{-2}$ directed towards West. Find the distance travelled in 6 seconds.
A.
40 m
B.
24 m
C.
32 m
D.
16 m
Q250
Allen
JEE-Main Pattern
MCQ
A car moving at 160 km/h when crosses the marker-0, driver applies brake and reduces its speed uniformly to 40 km/h at marker-2. The markers are spaced at equal distances along the road as shown below.
At which part of the track would the car have been traveling at instantaneous speed of 100 km/h?
A.
At marker-1
B.
Between marker-0 and marker-1
C.
Between marker-1 and marker-2
D.
More information required to decide.