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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q301 Allen 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
Q302 Allen 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
Q303 Allen 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
Q304 Allen 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
Q305 Allen 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
Q306 Allen 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.
$v = 4t^{-2} + 3t^{-1}$
Q307 Allen 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.
$y = (p + qt)rt$
Q308 Allen 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
Q309 Allen 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
Q310 Allen 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
Q311 Allen 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.
$a + \frac{b^{2}}{4c}$
Q312 Allen 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.
$4\hat{i}-2\hat{j}$
Q313 Allen 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
Q314 Allen 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.
$v = u + at$
Q315 Allen 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
Q316 Allen 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
Q317 Allen 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.
$14m/s^{2}$
Q318 Allen 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
Q319 Allen 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
Q320 Allen 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.
$4 \, m/s^{2}$
Q321 Allen 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
Q322 Allen 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.
Q323 Allen 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.
$\frac{7}{25}(3\hat{i} + 4\hat{j})$
Q324 Allen 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
Q325 Allen 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.