Motion

In our daily life we see some objects in motion e.g., walking men, moving cars, running trains, and some objects at rest e.g., furnitures, houses, trees, etc. In both the cases, we see that in motion, the position of objects change with time while at rest, the position of objects do not change with time.

Rest

If an object does not change its position with respect to its surroundings with time, then it is called at rest. e.g., a book lying on a desk is at rest, because its position with respect to the desk does not change with time.

Motion

If an object changes its position with respect to its surroundings with time, then it is called in motion. e.g., fish swims in water, car or bus moves on a road, train moves on the track, bird flying in air, etc.

Rest and motion are relative terms — an object in one situation can be at rest but in other situation same object can be in motion. e.g., if two cars are going side by side with the same velocity, then with respect to each other, they are in a state of rest, but with respect to trees and persons going on the road, they are in a state of motion.

Types of Motion of a Body

• Rectilinear and Translatory Motion: Motion along a straight line. e.g., sliding body on an inclined plane.
• Circular and Rotatory Motion: Motion along a circular path. e.g., string whirled in a loop. Rotatory motion: fan moving in the house.
• Oscillatory and Vibratory Motion: To and fro motion about a fixed point. Simple pendulum.

One, Two and Three Dimensional Motion

• One-Dimensional Motion: Position changes only in one direction (e.g., car on a straight road, freely falling body).
• Two-Dimensional Motion: Position changes in two directions (e.g., motion of planet around sun, projectile motion).
• Three-Dimensional Motion: Position changes in three directions (e.g., bird flying in sky, flying kite).

Some Basic Terms Related with Motion

Reference Point: A fixed point with respect to which the given body changes its position.

Position: Point in space where an object is present with respect to reference point.

Distance: Actual length of path covered by a moving body (scalar, SI unit: metre). Odometer measures distance.

Path Length: Length of curve joining initial and final positions along which particle actually moved.

Speed

Time rate of change of position: Speed(v) = Distance travelled(s) / Time taken(t). Scalar, SI unit m/s, dimensional formula [M⁰LT^-1]. Always positive.

Types of Speed

• Uniform speed (equal distances in equal intervals)
• Non-uniform speed
• Average speed = Total distance / Total time
• Instantaneous speed = lim_Δt→0 Δs/Δt = ds/dt

Displacement

Shortest straight line distance between initial and final position along with direction. Vector quantity. SI unit: metre. |Displacement| ≤ Distance.

Velocity

Time rate of change of displacement. Vector. SI unit m/s. Dimensional formula [M⁰LT^-1]. Types: uniform, non-uniform, average velocity = total displacement/total time, instantaneous velocity.

Relative velocity: v_ab = v_a - v_b (same direction); v_ab = v_a + v_b (opposite directions).

Acceleration

Time rate of change of velocity: a = (v - u)/t. SI unit m/s². Positive acceleration (increasing velocity), negative acceleration (deceleration/retardation).

• Uniform acceleration (constant change in velocity)
• Non-uniform acceleration
• Average acceleration = total change in velocity / total time
• Instantaneous acceleration

Uniform and Non-Uniform Motion

Uniform motion: equal distances in equal intervals of time. Non-uniform motion: unequal distances in equal intervals of time.

Graphical Representation of Motion

Displacement-Time Graph

• Object at rest: straight line parallel to time axis.
• Zero acceleration (uniform motion): straight line with positive slope.
• Uniform positive acceleration: curve with positive slope (increasing distance).
• Negative acceleration (retardation): curve with negative slope.

Velocity-Time Graph

• Constant velocity (zero acceleration): straight line parallel to time axis.
• Constant positive acceleration with initial velocity: straight line with positive slope.
• Constant positive acceleration zero initial velocity: straight line through origin.
• Constant negative acceleration: straight line with negative slope.
• Increasing acceleration: curve (velocity increasing non-uniformly).
• Decreasing acceleration: curve (velocity decreasing non-uniformly).

Slope of v-t graph → acceleration; Area under v-t graph → displacement.

Equations of Motion (Uniform Acceleration)

1. v = u + at    2. s = ut + ½ at²    3. v² - u² = 2as

Distance travelled in n^th second: s_n = u + ½ a (2n - 1)

Freely Falling Objects

Objects falling under gravity alone (g = 9.8 m/s² near earth surface). Equations of free fall:
v = u + gt,   h = ut + ½ gt²,   v² = u² + 2gh
If dropped (u=0), if thrown upward (g negative). In vacuum, all bodies fall with same acceleration irrespective of mass.

Motion in a Plane

Projectile Motion

Object thrown obliquely near earth surface follows parabolic path. Combination of horizontal (constant velocity) and vertical (gravity) motions.

• Horizontal component u_x = u cosθ, vertical component u_y = u sinθ
• Time of flight T = 2u sinθ / g
• Maximum height H = u² sin²θ / (2g)
• Range R = u² sin2θ / g; Maximum range at θ = 45°, R_max = u²/g
• Trajectory equation: y = (tanθ)x - (g x²)/(2u² cos²θ)

Circular Motion

Motion along a circular path. Uniform circular motion: constant speed but direction changes → acceleration exists.

• Time period T (time for one revolution)
• Frequency n = 1/T (Hz)
• Angular displacement θ = arc/radius (radian)
• Angular velocity ω = θ/t = 2π/T = 2πn
• Linear velocity v = rω
• Centripetal acceleration a_c = v²/r = rω² (towards centre)
• Angular acceleration α = dω/dt, tangential acceleration a_t = rα

In uniform circular motion, speed constant, velocity changes, centripetal acceleration is constant in magnitude but direction always towards centre.

Multiple Choice Questions (MCQs)