Kinematics Questions

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The study of motion of bodies not considering the cause of motion is called Kinematics. It deals with motion in a straight line, uniformly accelerated motion, freely falling body, objects projected vertically upwards, projectiles.

The following are the possible questions from kinematics.

Q1) Give two examples of the motion of big objects where the object can be treated as particle and where it cannot be?

Example of motion of big object treated as a particle 1) A space craft travelling towards moon. 2) Maximum displacement of bob suspended by a long string. Example for motion of big object where it cannot be treated as particle 1) A rain drop falling on the ground . 2) Earth revolving round the sun.

Q2) The state of motion is relative. Explain ?

A body is said to be at rest if it does not change its position with respect to its surroundings with passage of time. A body is said to be in motion if it changes its position with respect to its surroundings with passage of time. For example , A driver in a moving bus is at rest with respect to a person sitting inside the bus and is in motion with ...
... respect to a person outside the bus. Therefore rest and motion are relative.

Q3) Can an object have (i) a constant velocity even though its speed is changing (ii) a constant speed even though its velocity is changed?

(i) No. Because, a body is said to be moving with constant velocity when its magnitude and direction remains same.

(ii) Yes. In case of body moving a circular path.
Kinematics Questions

Q4) Give an example of a case where the velocity of an object is zero but its acceleration is not zero>

When a body is projected vertically up from ground its velocity will be zero at maximum height , but its acceleration is not zero.

Q5) Give an example of motion for which both the acceleration and velocity are negative?

(i) when a body moves from its mean position to extreme position in simple harmonic motion. Velocity is negative as it decreases and acceleration is negative as it is directed towards mean position.

(ii) A body thrown vertically upwards.

Q6) What is acceleration of a projectile at the top of its trajectory ?

The acceleration of a projectile at the top of its journey is vertically downwards. So the acceleration will be equal to the acceleration due to gravity. i.e., 'g' .

Q7) Can a body in free fall be in equilibrium? Explain?

No. A freely falling body is in accelerated motion. So some resultant force will act on it. Hence it is not in equilibrium i.e., forces are not balanced.

Q8) "Speed of a particle can be negative" . Is this statement correct ? If not why?

Speed is defined as the ratio of distance travelled and total time taken to cover it. As distance cannot be negative because it is a scalar quantity. Therefore speed also cannot be negative.

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More Kinematics Problem

Q9) A balloon starts from rest moves vertically upwards with an acceleration g/8 m.s-2 . A stone falls from the balloon after 8 seconds from the rest. Find the time taken by the stone to reach the ground. ( g = 9.8 m/s2 )

Let us find from what distance the stone begins to fall from the balloon

Substituting s = h , u = 0, a = g/8, t = 8secs.

S = ut + 1/2 at2

h = 1/2(g/8)(82 ) = 4g.

The velocity of the balloon at this height can be obtained from

v = u + at

= 0 + (g/8)8 = g

This becomes the initial velocity of the stone, as the stone falls from the balloon at the height 'h'. Substituting H = h = 4g, u = v = g , in

-H = ut - 1/2 gt2

-4g = gt - 1/2 gt2

t2 - 2t -8 = 0. solving for t , we get t = 4 and -2 seconds. Ignoring the negative value of time t = 4 seconds.

In this universe every object moves though some objects appear to be stationary they may be moving with respect to other objects. The study of motion of bodies, not considering the cause of motion is called Kinematics.

Velocity of a particle is the rate of change of displacement. We can represent the motion of a particle by position-time graph. For a particle moving along x-axis only x-coordinate varies with time; we have an x-t graph. Let us consider first that a particle continues to remain at a position with respect to the origin during the entire time interval. The particle is said to be at rest or stationary. Suppose a vehicle is at x = 50m with respect to the reference point all the time. Then the position-time graph is a parallel straight to the time axis.

Position Time Graph
Average Velocity Kinematics

Now we consider a particle moving back and forth along the x-axis. Suppose the particle has changed its position form x12 to x during a time interval `Delta`t = t2 - t1 , its displacement is `Delta`x = (x2 - x1 )i . x1 and x2 are the position vectors drawn from the origin along x-axis to the respective positions. As the motion is one dimensional , we can drop the vector notation and indicate the direction by means of +ve or -ve sign.

The average velocity of the particle is defined as the ratio of displacement `Deltax` to the time interval `Deltat` .

vx = `Deltax`/ `Deltat` = x2 - x1 / t2 - t1 .

Average velocity has dimensions of length divided by time i.e., [LT-1] and SI unit is ms-1 . Average velocity is independent of the path followed by the particle between the initial and final positions. No details of the motion are provided by the average velocity. It gives us only the result of the motion. The geometrical representation of average velocity is given in the following graph. A straight line is drawn between initial and final points on the curve. The average velocity fo the particle during a time interval `Deltat` is equal to the slope of the straight line joining initial and final points on the position-time graph.Position Time Graph

In variable motion the average velocity depends on the interval of the time during which the velocity is calculated. Only in uniform motion the average velocity is a constant value and is same for all the intervals of time during which the value is calculated. The magnitude of average velocity is equal to the average speed for motion along a straight line and it is a scalar quantity; but average velocity is a vector.
Instantaneous Velocity Kinematics

The average velocity does not describe the motion of the particle at a particular instant of a time during which time interval the average velocity is calculated. Hence to know how fast the particles moves at a particular instant of time we define Instantaneous velocity. The velocity of a particle at a particular instant of time (not during a finite time interval) is known as instantaneous velocity. The instantaneous velocity vx equals the limiting value of the average velocity `Deltax` `Deltat` as `Deltat` approaches 0. The instantaneous velocity is the rate of change of position with time.

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