Introduction — What is Motion?

Motion is the change in position of an object with time relative to a chosen reference point. In physics, describing motion requires specifying where an object is (position), how far it moves (distance), how fast it moves (speed) and the direction of motion (velocity). Chapter 8 (Motion) builds these concepts from simple definitions to graphical and mathematical descriptions used widely in mechanics.

Distance and Displacement

Distance is the total length of the path travelled by an object. It is a scalar quantity — only magnitude matters (no direction). Example: if you walk 2 m east then 3 m west, the total distance covered is 5 m.

Displacement is the shortest straight-line distance from the initial to the final position of the object, together with the direction. It is a vector quantity. In the same example, if you start at point A, walk 2 m east to point B, then 3 m west to point C, your displacement from A to C is 1 m west.

Speed and Velocity

Speed is the rate of change of distance with time. It is a scalar. Average speed = (total distance traveled) / (time taken).

Velocity is the rate of change of displacement with time. It is a vector quantity — both magnitude and direction are important. Average velocity = (displacement) / (time interval).

Instantaneous speed or velocity is the speed/velocity at a particular instant (read from speedometer or deduced from tangent to s–t graph).

Acceleration

Acceleration is the rate of change of velocity with time. If velocity changes (magnitude or direction), the object is accelerating. Acceleration may be positive (speeding up) or negative (slowing down — often called deceleration or retardation).

Acceleration has units of m/s² in SI. Uniform acceleration means acceleration is constant over time.

Equations of Motion (for Uniform Acceleration)

When acceleration a is uniform (constant), the following equations (derived from definitions) are used frequently:

Where:

• u = initial velocity (m/s)
• v = final velocity after time t (m/s)
• a = constant acceleration (m/s²)
• s = displacement in time t (m)
• t = time interval (s)

Graphs — Distance–Time and Velocity–Time

s–t (distance or displacement vs time) graph

The slope (gradient) of the s–t graph gives speed (or velocity if s is displacement). A straight line indicates uniform speed; a curved line indicates changing speed (acceleration).

v–t (velocity vs time) graph

The slope of the v–t graph gives acceleration. The area under the v–t graph between two times gives displacement during that interval.

Free Fall and Motion under Gravity (Qualitative)

Free fall is motion of an object under the influence of gravity alone (ignoring air resistance). Near Earth's surface, free-fall acceleration is nearly constant and is denoted by g (≈ 9.8 m/s²; sometimes taken as 9.8 or 10 m/s² depending on the level of approximation).

For objects falling from rest under gravity (downwards taken positive), you can use the same equations of motion with a = g and u = 0. For upward projection, acceleration is −g (negative) because gravity slows the object upward motion.

Relative Velocity (Conceptual)

Relative motion describes velocity of an object as observed from another moving object. If two objects move in the same straight line:

• Relative velocity of A w.r.t. B = v_A − v_B
• If they move in opposite directions, take signs into account (subtracting a negative adds).

Problem Solving Strategy — Quick Steps

1. Read the question carefully: identify knowns (u, v, a, s, t) and unknown to be found.
2. Choose coordinate and sign convention: decide which direction is positive (e.g., upward positive).
3. Select correct equation: pick one of the three equations of motion that includes knowns and unknown.
4. Keep units consistent: convert km/h to m/s (divide by 3.6) if necessary.
5. Sketch a simple diagram or graph: helps visualize displacements and directions.
6. Check your answer: does the magnitude and sign make sense physically?

Worked Examples (Typical NCERT style)

Formula Summary — Handy List

Common Mistakes to Avoid & Exam Tips

• Mixing up distance and displacement — remember direction matters for displacement only.
• For vertical motion under gravity, set sign convention clearly (take upward or downward as positive consistently).
• When using equations, ensure acceleration sign is correct. Upward motion has negative acceleration when gravity acts downward.
• Convert units before plugging into formulas — km/h → m/s by dividing by 3.6.
• In graphs, check whether s–t uses distance or displacement; if velocity changes sign, displacement can reduce while distance increases.
• Answer with correct units and appropriate significant figures where required.

Quick Practice Questions (for self-assessment)

1. A car moves with uniform speed of 72 km/h. Find its speed in m/s.
2. A ball dropped from rest falls freely. Write the equation to find distance after t seconds. (Neglect air resistance.)
3. A train starting from rest accelerates at 0.5 m/s² for 2 minutes. Find final velocity and distance covered.
4. A runner accelerates from 5 m/s to 9 m/s in 2 s. Find acceleration and distance covered in this interval.

(Answers: 1) 20 m/s. 2) s = ½ g t². 3) v = 60 m/s, s = ut + ½at² = 0 + 0.5×0.5×120² = compute carefully (convert minutes to seconds). 4) a = 2 m/s², s = ut + ½at² = 5×2 + 0.5×2×4 = 10 + 4 = 14 m.)

Summary — What to Remember

Chapter 8 (Motion) introduces the language of kinematics: distance, displacement, speed, velocity, acceleration and the equations used to describe linear motion under uniform acceleration. Mastering graphs (s–t and v–t), recognizing which equation to apply and practicing numerical problems are the keys to scoring well. NCERT problems provide a solid base — practice them, sketch clear diagrams and use consistent sign conventions.