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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q51 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
Displacement x of a particle is related to time t as $x = at + bt^{2} - ct^{3}$ where a, b and c are constants. The velocity of the particle when its acceleration is zero is given by:
A.
$a + \frac{b^{2}}{c}$
B.
$a + \frac{b^{2}}{2c}$
C.
$a + \frac{b^{2}}{3c}$
D.
$a + \frac{b^{2}}{4c}$
Q52 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
A particle moves along the curve $y = \frac{x^{2}}{2}$ . Here x varies with time as $x = \frac{t^{2}}{2}$ . Where x and y are measured in metre and t in second. At t = 2s, the velocity of the particle (in ms $^{-1}$ ) is:
A.
$2\hat{i}-4\hat{j}$
B.
$2\hat{i}+4\hat{j}$
C.
$4\hat{i}+2\hat{j}$
D.
$4\hat{i}-2\hat{j}$
Q53 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The velocity-time relation of an electron starting from rest is given by u = kt, where $k = 2 \, m/s^{2}$ . The distance traversed in 4 sec is:
A.
9m
B.
16 m
C.
27 m
D.
36 m
Q54 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The initial velocity of a particle is u (at t = 0) and the acceleration is given by f = atĀ². Which of the following relations is valid?
A.
$v = u + at^{2}$
B.
$v = u + \frac{at^{2}}{2}$
C.
$v = u + \frac{at^{3}}{3}$
D.
$v = u + at$
Q55 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
A particle is moving with a velocity of 10m/s towards east. After 20 s its velocity changes to 10m/s towards north. Its average acceleration is:-
A.
zero
B.
$\sqrt{2}$ m/s $^{2}$ towards N-W
C.
$\frac{1}{\sqrt{2}}$ m/s $^{2}$ towards N-E
D.
$\frac{1}{\sqrt{2}}$ m/s $^{2}$ towards N-W
Q56 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
Starting from rest, the acceleration of a particle is $a = 2(t - 1) \, \text{m/s}^2$ . The velocity of the particle at t = 5 s is :-
A.
15 m/s
B.
25 m/s
C.
5 m/s
D.
None of these
Q57 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
If the velocity of a particle is $(10 + 2t^{2})$ m/s, then the average acceleration of the particle between 2s and 5s is :-
A.
$2m/s^{2}$
B.
$4m/s^{2}$
C.
$12m/s^{2}$
D.
$14m/s^{2}$
Q58 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
If velocity of a particle is given by $v = (3t^{2} + 2)m/s$ , then average velocity in the interval $0 \leq t \leq 2sec$ :
A.
6 m/s
B.
8 m/s
C.
3 m/s
D.
4 m/s
Q59 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' which varies as $v = \alpha \sqrt{x}$ , then velocity of particle varies with time as: ( $\alpha$ is a constant)
A.
$v \propto t$
B.
$v \propto t^{2}$
C.
$v \propto \sqrt{t}$
D.
v = constant
Q60 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
If the velocity of a particle is given by $v = (180 - 16x)^{1/2}$ m/s, then its acceleration will be:
A.
Zero
B.
$8 \, m/s^{2}$
C.
$-8 \, m/s^{2}$
D.
$4 \, m/s^{2}$
Q61 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The acceleration of a particle moving in a straight line varies with its displacement as $a = 2S + 1$ . Velocity of the particle is zero at zero displacement. The relation between velocity and displacement is :-
A.
$v = S(S + 1)$
B.
$v = \sqrt{2S(S + 1)}$
C.
$v = \sqrt{S(S + 1)}$
D.
None of these
Q62 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
The position vector of a particle is given as $\vec{\mathrm{r}} = (t^2 - 4t + 6)\hat{\mathrm{i}} + (t^2)\hat{\mathrm{j}}$ . The time after which the velocity vector and acceleration vector becomes perpendicular to each other is equal to:
A.
1 sec.
B.
2 sec.
C.
1.5 sec.
D.
5 sec.
Q63 Allen 3. ACCELERATION, AVERAGE ACCELERATION & APPLICATION OF CALCULUS MCQ
At any instant of time acceleration and velocity of a particle are given by $\vec{a} = \hat{i} + \hat{j}$ & $\vec{v} = 6\hat{i} + 8\hat{j}$ , then rate of change of speed (component of acceleration along velocity) at the same instant will be:-
A.
$\frac{(3\hat{i} + 4\hat{j})}{25}$
B.
$\frac{6\hat{i} + 8\hat{j}}{25}$
C.
$\frac{7}{25}(3\hat{i} + 8\hat{j})$
D.
$\frac{7}{25}(3\hat{i} + 4\hat{j})$
Q64 Allen 4. CONSTANT ACCELERATION MOTION MCQ
If a body starts from rest, the time in which it covers a particular displacement with uniform acceleration is :
A.
inversely proportional to the square root of the displacement
B.
inversely proportional to the displacement
C.
directly proportional to the displacement
D.
directly proportional to the square root of the displacement
Q65 Allen 4. CONSTANT ACCELERATION MOTION MCQ
A body at rest is imparted motion to move in a straight line. It is then obstructed by an opposite force, then:
A.
the body may necessarily change direction
B.
the body is sure to slow down
C.
the body will necessarily continue to move in the same direction at the same speed
D.
none of the above.
Q66 Allen 4. CONSTANT ACCELERATION MOTION MCQ
If a car at rest accelerates uniformly to a speed of 144 km/h in 40 seconds, it covers a distance of :
A.
200 m
B.
800 m
C.
1440 m
D.
2980 m
Q67 Allen 4. CONSTANT ACCELERATION MOTION MCQ
If a car at rest accelerates uniformly and attains a speed of 54 km/h in 10s, then it covers a distance of
A.
75 m
B.
100 m
C.
200 m
D.
400 m
Q68 Allen 4. CONSTANT ACCELERATION MOTION MCQ
If a train travelling at 72 km/h is to be brought to rest in a distance of 100 m, then its retardation should be:
A.
$20 \, m/s^{2}$
B.
$2 \, m/s^{2}$
C.
$10 \, m/s^{2}$
D.
$1 \, m/s^{2}$
Q69 Allen 4. CONSTANT ACCELERATION MOTION MCQ
Initially a body is at rest. If its acceleration is $5ms^{-2}$ then the distance travelled in the $5^{th}$ second is:-
A.
86.6 m
B.
87.5 m
C.
88 m
D.
22.5 m
Q70 Allen 4. CONSTANT ACCELERATION MOTION MCQ
A car starts from rest travelling with constant acceleration. If distance covered by it in $10^{\text{th}}$ second of its journey is 19m, what will be the acceleration of car?
A.
$4 \mathrm{~m} / \mathrm{s}^{2}$
B.
$3 \mathrm{~m} / \mathrm{s}^{2}$
C.
$2 \mathrm{~m} / \mathrm{s}^{2}$
D.
$1 \mathrm{~m} / \mathrm{s}^{2}$
Q71 Allen 4. CONSTANT ACCELERATION MOTION MCQ
A car starts from rest and moves with constant acceleration. The ratio of the distance covered in the $n^{th}$ second to that covered in n seconds is:
A.
$\frac{2}{n^{2}} - \frac{1}{n}$
B.
$\frac{2}{n^{2}} + \frac{1}{n}$
C.
$\frac{2}{n} - \frac{1}{n^{2}}$
D.
$\frac{2}{n} + \frac{1}{n^{2}}$
Q72 Allen 4. CONSTANT ACCELERATION MOTION MCQ
A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 5th second?
A.
$\frac{7}{5}$
B.
$\frac{5}{7}$
C.
$\frac{7}{9}$
D.
$\frac{3}{7}$
Q73 Allen 4. CONSTANT ACCELERATION MOTION MCQ
A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20m. If the velocity of the car is 40 m/s. It can be stopped by this force in:
A.
$\frac{20}{3}$ m
B.
320 m
C.
60 m
D.
180 m
Q74 Allen 4. CONSTANT ACCELERATION MOTION MCQ
A car moving with a speed of 40 km/h can be stopped by applying brakes after at least 2m. If the same car is moving with a speed of 120 km/h., what is the minimum stopping distance?
A.
2 m
B.
4 m
C.
6 m
D.
18 m
Q75 Allen 4. CONSTANT ACCELERATION MOTION MCQ
The velocity acquired by a body moving with uniform acceleration is 30 m/s in 2 seconds and 50 m/s in 4 seconds. The initial velocity is:
A.
zero
B.
2 m/s
C.
4 m/s
D.
10 m/s