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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q276 Allen DISTANCE & DISPLACEMENT MCQ
A person walks 80 m east, then turns right through angle $143^{\circ}$ walks further 50 m and stops. His position relative to the starting point is
A.
50 m, $53^{\circ}$ east of south
B.
50 m, $53^{\circ}$ south of east
C.
30 m, $37^{\circ}$ south of east
D.
30 m, $53^{\circ}$ south of east
Q277 Allen DISTANCE & DISPLACEMENT MCQ
A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward, followed by 5 steps forward and 3 steps backward and so on. Each step is one meter long and takes one second. There is a pit on the road 13 meters away from the starting point. The drunkard will fall into the pit after:
A.
29 s
B.
21 s
C.
37s
D.
31 s
Q278 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A train covers the first half of the distance between two stations with a speed of 30 km/h and the other half with 70 km/h. Then its average speed is:
A.
50 km/h
B.
48 km/h
C.
42 km/h
D.
100 km/h
Q279 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
Select the correct statements from the following. S1. Average velocity is path length divided by time interval. S2. In general, average speed ā‰„ |average velocity| S3. A particle moving in a given direction with a non-zero velocity can have zero speed. S4. The magnitude of average velocity is the average speed.
A.
Sā‚
B.
Sā‚‚
C.
Sā‚ƒ
D.
Sā‚„
Q280 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
The magnitude of average velocity is equal to the average speed when a particle moves :
A.
on a curved path
B.
in the same direction
C.
with constant acceleration
D.
with constant retardation
Q281 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A man walks for some time 't' with velocity (v) due east. Then he walks for same time 't' with velocity (v) due north. The average speed of the man is:
A.
2v
B.
$\sqrt{2}$ v
C.
v
D.
$\frac{v}{\sqrt{2}}$
Q282 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A car travels a distance $d$ on a straight road in two hours and then returns to the starting point in next three hours. Its average speed and average velocity is:
A.
$\frac{d}{5}, 0$
B.
$\frac{2d}{5}, 0$
C.
$\frac{5d}{6}, \frac{d}{5}$
D.
none of these
Q283 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A particle moves in the east direction with 15 m/sec for 2 sec then northwards with 5 m/s for 8 sec. Average velocity of the particle is:-
A.
1 m/s
B.
5 m/s
C.
7 m/s
D.
10 m/s
Q284 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A man walks on an equilateral triangle along path ABC with constant speed then the ratio of average speed and magnitude of average velocity for A to C :-
A.
1
B.
2
C.
$\frac{1}{2}$
D.
None
Q285 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A car runs at constant speed on a circular track of radius 10 m taking 6.28s on each lap (i.e. round). The average speed and average velocity for half lap is :
A.
Velocity $20/\pi$ m/s, speed 10 m/s
B.
Velocity zero, speed 10 m/s
C.
Velocity zero, speed zero
D.
Velocity 10 m/s, speed zero
Q286 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A particle moves in straight line in same direction for 20 sec. with velocity $3\mathrm{m / s}$ and then moves with velocity $4\mathrm{m / s}$ for another 20 sec. and finally moves with velocity $5\mathrm{m / s}$ for next 20 sec. What is the average velocity of the particle?
A.
$3\mathrm{m / s}$
B.
$4\mathrm{m / s}$
C.
$5\mathrm{m / s}$
D.
Zero
Q287 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
An object travels 10 km at a speed of 100 m/s and another 10 km at 50 m/s. The average speed over the whole distance is :-
A.
75 m/s
B.
55 m/s
C.
66.7 m/s
D.
33.3 m/s
Q288 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A body has speed V, 2V and 3V in first 1/3 part of total travelled distance S, second 1/3 part of S and third 1/3 part of S respectively. Its average speed will be :-
A.
V
B.
2V
C.
$\frac{18}{11}\mathrm{V}$
D.
$\frac{11}{18}\mathrm{V}$
Q289 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A body covers one-third of the time with a velocity $v_{1}$ the second one-third of the time with a velocity $v_{2}$ , and the last one-third of the time with a velocity $v_{3}$ . The average velocity is:
A.
$\frac{v_{1} + v_{2} + v_{3}}{3}$
B.
$\frac{3v_{1}v_{2}v_{3}}{v_{1}v_{2} + v_{2}v_{3} + v_{3}v_{1}}$
C.
$\frac{v_{1}v_{2}+v_{2}v_{3}+v_{3}v_{1}}{3}$
D.
$\frac{v_{1}v_{2}v_{3}}{3}$
Q290 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
If a car cover $2/5^{th}$ of total distance with $v_{1}$ speed and $3/5^{th}$ distance with $v_{2}$ speed then the average speed is:
A.
$\frac{1}{2}\sqrt{v_{1}v_{2}}$
B.
$\frac{v_{1}+v_{2}}{2}$
C.
$\frac{2v_{1}+v_{2}}{v_{1}+v_{2}}$
D.
$\frac{5v_{1}v_{2}}{3v_{1}+2v_{2}}$
Q291 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A particle moving in a straight line covers half the distance with speed of 10 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is:
A.
8.0 m/s
B.
12.0 m/s
C.
10.0 m/s
D.
7.5 m/s
Q292 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A point object traverses half the distance with velocity $v_{0}$ . The remaining part of the distance is covered with velocity $v_{1}$ for the half time and with velocity $v_{2}$ for the rest half. The average velocity of the object for the whole journey is
A.
$2\mathrm{v}_1(\mathrm{v}_0 + \mathrm{v}_2) / (\mathrm{v}_0 + 2\mathrm{v}_1 + 2\mathrm{v}_2)$
B.
$2\mathrm{v}(\mathrm{v}_0 + \mathrm{v}_1) / (\mathrm{v}_0 + \mathrm{v}_1 + \mathrm{v}_2)$
C.
$2\mathrm{v}_0(\mathrm{v}_1 + \mathrm{v}_2) / (\mathrm{v}_1 + \mathrm{v}_2 + 2\mathrm{v}_0)$
D.
$2\mathrm{v}_2(\mathrm{v}_0 + \mathrm{v}_1) / (\mathrm{v}_1 + 2\mathrm{v}_2 + \mathrm{v}_0)$
Q293 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A scooter going due east at $10 \, ms^{-1}$ turns in right side through an angle of $90^{\circ}$ . If the speed of the scooter remains unchanged in taking this turn, the change in the velocity of the scooter is :-
A.
$20.0 \, ms^{-1}$ in south-west direction
B.
Zero
C.
$10.0 \, ms^{-1}$ in south-east direction
D.
$14.14 \, ms^{-1}$ in south-west direction
Q294 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
A person is moving in a circle of radius r with constant speed V. The change in velocity in moving from A to B is
A.
$2\mathrm{V}\cos 40^{\circ}$
B.
$2\mathrm{V}\sin 40^{\circ}$
C.
$2\mathrm{V}\cos 20^{\circ}$
D.
$2\mathrm{V}\sin 20^{\circ}$
Q295 Allen SPEED & VELOCITY, AVERAGE SPEED & AVERAGE VELOCITY MCQ
An insect crawls a distance of 4m along north in 10 s and then a distance of 3m along east in 5 s. The average velocity of the insect is:
A.
$\frac{7}{15}$ m/s
B.
$\frac{1}{5}$ m/s
C.
$\frac{1}{3}$ m/s
D.
$\frac{4}{5}$ m/s
Q296 Allen ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The position x of a particle varies with time (t) as $x = at^{2} - bt^{3}$ . The velocity at time t of the particle will be equal to zero, where t is equal to:
A.
$\frac{2a}{3b}$
B.
$\frac{a}{b}$
C.
$\frac{a}{3b}$
D.
$\frac{a}{2b}$
Q297 Allen ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
If x denotes displacement in time t and x = a sint, then acceleration is:
A.
a cos t
B.
- a cos t
C.
a sin t
D.
- a sin t
Q298 Allen ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The motion of a particle is described by the equation $x = a + bt^{2}$ where a = 15 cm and $b = 3 \, cm/sec^{2}$ . Its acceleration at time 3 sec will be :-
A.
$36 \, cm/sec^{2}$
B.
$18 \, cm/sec^{2}$
C.
$6 \, cm/sec^{2}$
D.
$32 \, cm/sec^{2}$
Q299 Allen ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
Equation of displacement for a particle is $s = 3t^{3} + 7t^{2} + 14t + 8 \, m$ . Its acceleration at time t = 2 sec is :-
A.
$10 \, m/s^{2}$
B.
$16 \, m/s^{2}$
C.
$25 \, m/s^{2}$
D.
$50 \, m/s^{2}$
Q300 Allen ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
A body is moving according to the equation $x = at^{2} + bt - c$ . Then its instantaneous speed is given by :-
A.
$a + 2b + 3ct$
B.
$a + 2bt - 3ct^{2}$
C.
2b - 6ct
D.
2at + b