“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*v*_{1}and*v*_{2}respectively.**What is the average speed of the car for the entire trip from station A to station B?**
(a) √(

*v*_{1}*v*_{2})
(b) (

*v*_{1}*v*_{2})/(*v*_{1}+*v*_{2})
(c) (

*v*_{1}+*v*_{2})/2
(d) (

*v*_{1}*v*_{2})/(*v*_{1}–*v*_{2})
(e) (2

*v*_{1}*v*_{2})/(*v*_{1}+*v*_{2})
The times taken for
covering the first and second halves of the trip are

*d*/2*v*_{1}and*d*/2*v*_{2}respectively.
Therefore, the
total time taken to cover the entire istance

*d*is (*d*/2*v*_{1 }+*d*/2*v*_{2}) =*d*[(1/2*v*_{1})_{ }+ (1/2*v*_{2})] =*d*[(*v*_{1}+*v*_{2})/2*v*_{1}*v*_{2}]
The average speed

*v*for he entire trip is is given by*v = d/d*[(

*v*

_{1}+

*v*

_{2})/2

*v*

_{1}

*v*

_{2}] = (2

*v*

_{1}

*v*

_{2})/(

*v*

_{1}+

*v*

_{2})

(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

**F**and_{1}**F**with their lines of action in the XY plane and acting on a particle.P._{2}
If

**F**_{1}**=**a_{1}**î +**b_{1}**ĵ**
and

**F**a_{2 }=_{2}**î +**b_{2}**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) a

_{1}, b_{1}, a_{2}, and b_{2}are positive.
(b) a

_{1 }and b_{1}are negative where as a_{2}and b_{2}are positive.
(c) a

_{1}is negative where as b_{1}, a_{2}, and b_{2}are positive.
(d) a

_{1}, b_{1}and a_{2}are positive where as b_{2}is positive.
(e) a

_{1}, b_{1}, a_{2}, and b_{2}are negative.
Imagine the
rectangular components of

**F**and_{1}**F**. You can easily see that the x-component of_{2}**F**is along the negative x-direction while the y-component is along the positive y-direction. The x-component of_{1}**F**is along the positive x-direction while the y-component is along the positive y-direction._{2}
This means that a

_{1}is negative where as b_{1}, a_{2}, and b_{2}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).