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Kinematics-1D

700 Questions Start Allen Test
All Exams Allen Objective Errorless
Q426 Allen GRAPHICAL ANALYSIS MCQ
A train takes 4 min. to go between stations 2.25 km apart starting and finishing at rest. The acceleration is uniform for the first 40 sec and the deceleration is uniform for the last 20 sec. Assuming the velocity to be constant for the remaining time, then maximum speed of the train is :-
A.
75 m/sec
B.
18.75 m/sec
C.
37.5 m/sec
D.
10.7 m/sec
Q427 Allen GRAPHICAL ANALYSIS MCQ
A car accelerates from rest at a constant rate of $2 \, m/s^{2}$ for some time. Then, it retards at a constant rate of $4 \, m/s^{2}$ and comes to rest. If it remains in motion for 3 seconds, then the maximum speed attained by the car is:
A.
2 m/s
B.
3 m/s
C.
4 m/s
D.
6 m/s
Q428 Allen GROUND TO GROUND PROJECTION MCQ
In the graph shown in fig. time is plotted along x-axis. Which quantity associated with a projectile motion is plotted along the y-axis?
A.
kinetic energy
B.
momentum
C.
horizontal velocity
D.
none of the above
Q429 Allen GROUND TO GROUND PROJECTION MCQ
For ground to ground projection following curves are given :-
(a)

(b)

(c)

(d)

Find incorrect one.
A.
a
B.
b
C.
c
D.
d
Q430 Allen GROUND TO GROUND PROJECTION MCQ
If air resistance is not considered in projectile motion, the horizontal motion takes place with
A.
constant velocity
B.
constant acceleration
C.
constant retardation
D.
variable velocity
Q431 Allen GROUND TO GROUND PROJECTION MCQ
In a projectile motion, the velocity:-
A.
is always perpendicular to the acceleration
B.
is never perpendicular to the acceleration
C.
is perpendicular to the acceleration for one instant only
D.
is perpendicular to the acceleration for two instants
Q432 Allen GROUND TO GROUND PROJECTION MCQ
In projectile motion, the modulus of rate of change of velocity-
A.
is constant
B.
first increases then decreases
C.
first decreases then increases
D.
None of the above
Q433 Allen GROUND TO GROUND PROJECTION MCQ
Which of the following quantities remains constant during projectile motion?
(A) Average velocity between two points.
(B) Average speed between two points
(C) $\frac{d\vec{v}}{dt}$ (D) $\frac{d^{2}}{dt^{2}}(\vec{v})$
A.
only A
B.
only C
C.
A and C
D.
C and D
Q434 Allen GROUND TO GROUND PROJECTION MCQ
A bomb is fired from a cannon with a velocity of 1000 m/s making an angle of $30^{\circ}$ with the horizontal. What is the time taken by the bomb to reach at the highest point-
A.
11 sec
B.
23 sec
C.
38 sec
D.
50 sec
Q435 Allen GROUND TO GROUND PROJECTION MCQ
If time of flight of a projectile is 10 seconds. Range is 500 meters. The maximum height attained by it will be :-
A.
125 m
B.
50 m
C.
100 m
D.
150 m
Q436 Allen GROUND TO GROUND PROJECTION MCQ
A body is thrown with a velocity of 19.6 m/s making an angle of $30^{\circ}$ with the horizontal. It will hit the ground after a time:ā€”
A.
3 s
B.
2 s
C.
1.5 s
D.
1 s
Q437 Allen GROUND TO GROUND PROJECTION MCQ
If a projectile is fired at an angle $\theta$ to the vertical with velocity $u$ , then maximum height attained is given by:
A.
$\frac{u^2 \cos \theta}{2g}$
B.
$\frac{u^2 \sin^2 \theta}{2g}$
C.
$\frac{u^2 \sin^2 \theta}{g}$
D.
$\frac{u^2 \cos^2 \theta}{2g}$
Q438 Allen GROUND TO GROUND PROJECTION MCQ
At the uppermost point of a projectile its velocity and acceleration are at an angle of:-
A.
$180^{\circ}$
B.
$90^{\circ}$
C.
$60^{\circ}$
D.
$45^{\circ}$
Q439 Allen GROUND TO GROUND PROJECTION MCQ
Two projectiles are projected with velocity $v_{A}$ , $v_{B}$ at angles $\theta_{A}$ (from horizontal) and $\theta_{B}$ (from vertical) as shown in the figure below, such that $v_{A} > v_{B}$ but having same horizontal component of velocity. Which of the following can not be correct?
A.
$\mathrm{T_A > T_B}$
B.
$\mathrm{H_A > H_B}$
C.
$\mathrm{R_A > R_B}$
D.
$\mathrm{R_B > R_A}$
Q440 Allen GROUND TO GROUND PROJECTION MCQ
A player throws a ball that reaches to the another player in 4s. If the height of each player is 1.5m, the maximum height attained by the ball from the ground level is:
A.
19.6 m
B.
21.1 m
C.
23.6 m
D.
25.1 m
Q441 Allen GROUND TO GROUND PROJECTION MCQ
A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with speed v. While rising up the magnitude of the velocity after t seconds will be:
A.
$\sqrt{(v\cos\theta)^2 + (v\sin\theta)^2}$
B.
$\sqrt{(v\cos\theta - v\sin\theta)^2 - gt}$
C.
$\sqrt{v^2 + g^2t^2 - (2v\sin\theta)gt}$
D.
$\sqrt{v^2 + g^2t^2 - (2v\cos\theta)gt}$
Q442 Allen GROUND TO GROUND PROJECTION MCQ
A particle is fired with velocity u making $\theta$ angle with the horizontal. What is the magnitude of change in velocity when it returns to the ground.
A.
u cos $\theta$
B.
u
C.
2u sin $\theta$
D.
(u cos $\theta - u$ )
Q443 Allen GROUND TO GROUND PROJECTION MCQ
In the above, the change in speed is:
A.
u cos Īø
B.
0
C.
u sin Īø
D.
(u cosĪø - u)
Q444 Allen GROUND TO GROUND PROJECTION MCQ
The angle which the velocity vector of a projectile, will make with the vertical after time t of its being thrown with a velocity v at an angle $\theta$ to the horizontal, is:
A.
$\theta$
B.
$\tan^{-1}\left(\frac{\theta}{t}\right)$
C.
$\tan^{-1}\left(\frac{v\cos\theta}{v\sin\theta-gt}\right)$
D.
$\tan^{-1}\left(\frac{v\sin\theta-gt}{v\cos\theta}\right)$
Q445 Allen GROUND TO GROUND PROJECTION MCQ
At a height 0.4 m from the ground, the velocity of a projectile in vector form is: $\vec{v}=(6\hat{i}+2\hat{j})$ m/s. The angle of projection from horizontal is $(g=10\mathrm{~m/s^{2}})$:-
A.
$45^{\circ}$
B.
$60^{\circ}$
C.
$30^{\circ}$
D.
$\tan^{-1}(3/4)$
Q446 Allen GROUND TO GROUND PROJECTION MCQ
In case of a projectile fired at an angle $60^{\circ}$ to the horizontal with velocity u, the horizontal range is:
A.
$\frac{u^{2}}{g}$
B.
$\frac{\sqrt{3}u^{2}}{2g}$
C.
$\frac{2u^{2}}{g}$
D.
$\frac{u^{2}}{g^{2}}$
Q447 Allen GROUND TO GROUND PROJECTION MCQ
If the instantaneous velocity of a particle projected as shown in figure is given by $\vec{v}=a\hat{i}+(b-ct)\hat{j}$ where a, b and c are positive constants, the range on the horizontal plane will be :
A.
2ab/c
B.
ab/c
C.
ac/b
D.
a/2bc
Q448 Allen GROUND TO GROUND PROJECTION MCQ
A projectile is thrown from a point in a horizontal plane such that its horizontal and vertical velocity components are 9.8 m/s and 4.9 m/s respectively. Its horizontal range is:
A.
4.9 m
B.
9.8 m
C.
19.6 m
D.
39.2 m
Q449 Allen GROUND TO GROUND PROJECTION MCQ
A projectile is projected with initial velocity $(5\hat{i}+12\hat{j})$ m/s. If g = 10 ms $^{-2}$ , then horizontal range is :
A.
4.8 metre
B.
9.6 metre
C.
19.2 metre
D.
12 metre
Q450 Allen GROUND TO GROUND PROJECTION MCQ
A shell is fired vertically upwards with a velocity $v_{1}$ from the deck of a ship moving with a speed $v_{2}$ . A person on the shore observes the motion of the shell as a parabola. Its horizontal range is given by:
A.
$\frac{2v_{1}^{2}v_{2}}{g}$
B.
$\frac{2v_{1}v_{2}^{2}}{g}$
C.
$\frac{2v_{1}v_{2}}{g}$
D.
$\frac{2v_{1}^{2}v_{2}^{2}}{g}$