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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q26 Allen 2. 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
Q27 Allen 2. 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
Q28 Allen 2. 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.
$\frac{11}{18}\mathrm{V}$
Q29 Allen 2. 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.
$\frac{v_{1}v_{2}v_{3}}{3}$
Q30 Allen 2. 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.
$\frac{5v_{1}v_{2}}{3v_{1}+2v_{2}}$
Q31 Allen 2. 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
Q32 Allen 2. 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.
$2\mathrm{v}_2(\mathrm{v}_0 + \mathrm{v}_1) / (\mathrm{v}_1 + 2\mathrm{v}_2 + \mathrm{v}_0)$
Q33 Allen 2. 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
Q34 Allen 2. 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.
$2\mathrm{V}\sin 20^{\circ}$
Q35 Allen 2. 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
Q36 Allen 3. 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.
$\frac{a}{2b}$
Q37 Allen 3. 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
Q38 Allen 3. 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.
$32 \, cm/sec^{2}$
Q39 Allen 3. 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.
$50 \, m/s^{2}$
Q40 Allen 3. 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
Q41 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The relation $t = \sqrt{x} + 3$ describes the position of a particle where x is in meters and t is in seconds. The acceleration of particle is:
A.
$2 \, m/s^{2}$
B.
$4 \, m/s^{2}$
C.
$5 \, m/s^{2}$
D.
zero
Q42 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The displacement of a particle is given by $y = a + bt + ct^{3}$ . The initial velocity and acceleration are respectively:
A.
b, 0
B.
-b, 2c
C.
b, 2c
D.
2c, -4d
Q43 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
Equation of a particle moving along the x axis is $x = u(t - 2) + a(t - 2)^{2}$
A.
the initial velocity of the particle is u
B.
the acceleration of the particle is a
C.
the acceleration of the particle is 2a
D.
at t = 2 particle is not at origin
Q44 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
If for a particle position $x \propto t$ then:
A.
velocity is constant
B.
acceleration is non zero
C.
acceleration is variable
D.
None of these
Q45 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The velocity of a body depends on time according to the equation $= 20 + 0.1t$ . The body has:
A.
uniform acceleration
B.
uniform retardation
C.
non-uniform acceleration
D.
zero acceleration
Q46 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
Which of the following relations representing velocity of a particle describes motion with constant acceleration?
A.
v = 6 - 7 t
B.
$v = 3t^{2} + 5t^{3} + 7$
C.
$v = 9t^{2} + 8$
D.
$v = 4t^{-2} + 3t^{-1}$
Q47 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
Which of the following equations represents the motion of a body moving with constant finite velocity? in these equations, y denotes the displacement in time t and p, q and r are arbitrary constants:
A.
$y = (p + qt)^{2} (r + pt)$
B.
$y = p + tqr$
C.
$y = (p + t)(q + t)(r + 1)$
D.
$y = (p + qt)rt$
Q48 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The displacement of a particle starting from rest (at t=0) is given by $s = 6t^{2} - t^{3}$ The time when the particle will attain zero acceleration is :
A.
2s
B.
8s
C.
12s
D.
16s
Q49 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The displacement of a particle varies with time according to the relation $x = \frac{k}{b}[1 - e^{-bt}]$ . Then the velocity of the particle is:
A.
$k(e^{-bt})$
B.
$\frac{k}{b^{2}e^{-bt}}$
C.
$kbe^{-bt}$
D.
None of these
Q50 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS 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 displacement when the acceleration is zero is:
A.
3 m
B.
-12
C.
42 m
D.
-6 m