“Being ignorant is not so much a shame, as being unwilling to learn.”
– Benjamin Franklin
Many questions
(with solution) involving kinematics in one dimension and two dimensions have
been posted on this site earlier. You may click on the label ‘kinematics’ below
this post to access them. After obtaining the first result, you will have to
click on the ‘older posts’ tab to access all the posts in this section.
Alternatively you may try a search for ‘kinematics’ using the search box
provided on this page.
Today we shall
discuss a few more multiple choice practice questions on kinematics:
(1) A car travels
from station A and to station B separated by a distance of d km. The average speeds of the car while covering the first and
second halves of the distance are v1
and v2 respectively. What
is the average speed of the car for the entire trip from station A to station B?
(a) √(v1v2)
(b) (v1v2)/(v1+v2)
(c) (v1+v2)/2
(d) (v1v2)/(v1–v2)
(e) (2v1v2)/(v1+v2)
The times taken for
covering the first and second halves of the trip are d/2v1 and d/2v2
respectively.
Therefore, the
total time taken to cover the entire istance d is (d/2v1 + d/2v2) = d[(1/2v1) + (1/2v2)]
= d[(v1+v2)/2v1v2]
The average speed v for he entire trip is is given by
v
= d/d[(v1+v2)/2v1v2] = (2v1v2)/(v1+v2)
(2) An object has
acceleration. Then
(a) its speed must be decreasing
(b) its speed must be increasing
(c) its speed must be decreasing or increasing
(d) its direction must be changing
(e) its speed or direction must be changing
An object moving
with varying speed has acceleration. But this does not mean that all
accelerated objects must move with a varying speed. For instance, an object in
uniform circular motion has constant speed, even though it has a centripetal
acceleration. Its direction of motion changes continuously and it is the change
in direction that makes it an accelerated
object.
For an object to be
in accelerated motion, it is enough that its speed or direction of motion
changes. Therefore, the correct option is (e).
(3) A bullet is fired
from a gun in a direction inclined at angle θ with respect to the horizontal ground. Which one among the
following graphs represents the plot of the vertical velocity v of the bullet against time t between the instant of firing and the
instant just before the bullet hits the ground? (Take the upward direction as
positive).
At the instant of
firing, the bullet has the highest vertical velocity. When the bullet rises up,
its vertical velocity goes on decreasing linearly (because of gravity) and at
the highest point of its trajectory the vertical velocity becomes zero. The bullet
then starts falling down with
linearly increasing speed. In other words, the vertical velocity of the bullet
becomes negative and its magnitude goes on increasing until it hits the ground.
The vertical
velocity of the bullet as a function of time is therefore correctly represented
by graph (b).
(4) The adjoining
figure shows forces F1
and F2 with their lines
of action in the XY plane and acting on a particle.P.
If F1 = a1 î + b1 ĵ
and F2 = a2 î + b2 ĵ where î and
ĵ are unit vectors in the x-direction and y-direction respectively, which
one among the following statements is correct?
(a) a1, b1, a2, and b2 are positive.
(b) a1 and b1 are negative where
as a2 and b2 are positive.
(c) a1 is negative where as b1, a2, and b2 are positive.
(d) a1, b1 and a2
are positive where as b2 is positive.
(e) a1, b1, a2, and b2 are negative.
Imagine the
rectangular components of F1
and F2. You can easily
see that the x-component of F1
is along the negative x-direction while the y-component is along the positive
y-direction. The x-component of F2
is along the positive x-direction while the y-component is along the
positive y-direction.
This means that a1
is negative where as b1, a2,
and b2 are positive
[Option (c)].
(5) A small object at the
foot of a smooth inclined plane AB (Fig.) is projected up along the inclined
plane with an initial speed v. The
object returns before reaching the top of the inclined plane and after reaching
the foot of the plane, it moves further
along a smooth horizontal surface AC. Which one among the following graphs
represents the variation of the speed v of
the object against time t?
of the object
therefore gets decreased uniformly and becomes zero when the object reaches its
highest position on the incline. Then the object retraces its path with
uniformly increasing speed until it reaches the foot of the incline. Then it
moves along the horizontal surface AC with uniform speed.
The above facts are
correctly represented by the graph (d).
