Motion Class 9 Chapter Notes

Key points

• Motion is always described with respect to a reference point; an object may be at rest for one observer and in motion for another.
• Distance is the actual path length travelled; displacement is the shortest straight-line change in position from initial to final point.
• Speed = distance/time and velocity = displacement/time. Speed is scalar; velocity is vector.
• Uniform motion means equal distances are covered in equal intervals of time; non-uniform motion means unequal distances in equal intervals or equal distances in unequal intervals.
• Acceleration is rate of change of velocity: a = (v - u)/t. Its SI unit is m/s².
• For uniformly accelerated straight-line motion, use v = u + at, s = ut + 1/2 at², and v² - u² = 2as.
• Slope of a distance-time graph gives speed; slope of a velocity-time graph gives acceleration.
• Area under a velocity-time graph gives displacement, not acceleration.
• Uniform circular motion is accelerated motion because direction of velocity changes continuously even if speed remains constant.

Understanding motion in one page

In Physics, motion means change in position of an object with time, but position has meaning only when a reference point or origin is fixed. For example, a passenger sitting in a moving bus is at rest with respect to the bus seat but in motion with respect to a tree on the roadside. This is why rest and motion are called relative terms. To describe motion properly, Class 9 focuses on measurable quantities: distance, displacement, speed, velocity and acceleration. Distance tells how much path is covered, while displacement tells the straight-line change from start to end. Speed tells how fast distance is covered, while velocity tells how fast displacement changes in a particular direction. If velocity changes with time, the body has acceleration. Most numericals in this chapter become easy if you identify the given values u, v, a, t and s, write SI units, then choose the correct equation of motion.

Definitions glossary

Rest

A body is said to be at rest if its position does not change with time with respect to a chosen reference point.

Motion

A body is in motion if its position changes with time with respect to a chosen reference point.

Distance

The total length of the actual path travelled by a body. It is a scalar quantity and is never negative.

Displacement

The shortest straight-line distance between initial and final positions in a specified direction. It is a vector quantity.

Speed

Distance travelled per unit time. Speed = distance/time. SI unit: metre per second or m/s.

Velocity

Displacement per unit time in a given direction. Velocity = displacement/time. SI unit: m/s.

Acceleration

Rate of change of velocity with time. Acceleration = change in velocity/time. SI unit: m/s².

Uniform motion

Motion in which a body covers equal distances in equal intervals of time.

Uniform acceleration

Acceleration in which velocity changes by equal amounts in equal intervals of time.

Formula sheet for Motion

Distance vs displacement and speed vs velocity

How to solve motion numericals quickly

1. List the data —
2. Check the type of motion —
3. Choose the formula by missing variable —
4. Apply sign convention —
5. Write final answer with unit —

Graph reading: the most scoring part

Graphs convert motion data into a visual form. In a distance-time graph, the slope shows speed. A straight sloping line means uniform speed, a curved line means non-uniform speed, and a horizontal line means the object is at rest. In a velocity-time graph, the slope shows acceleration. A horizontal velocity-time graph means constant velocity and zero acceleration. A straight rising line means uniform acceleration. The area under a velocity-time graph gives displacement because velocity × time = displacement. For Class 9 exams, always label axes with units, identify whether the graph is distance-time or velocity-time, and mention what slope or area represents.

Worked mini-examples

• {"title":"Average speed","bodyMarkdown":"A cyclist covers 120 m in 20 s. Average speed = distance/time = 120/20 = 6 m/s."}
• {"title":"Acceleration","bodyMarkdown":"A car speeds up from 10 m/s to 25 m/s in 5 s. a = (v - u)/t = (25 - 10)/5 = 3 m/s²."}
• {"title":"Using v² - u² = 2as","bodyMarkdown":"A body starts from rest and accelerates at 2 m/s² for 25 m. Here u = 0, a = 2, s = 25. v² = 2as = 2 × 2 × 25 = 100, so v = 10 m/s."}

Must remember: equations of motion conditions

• The equations v = u + at, s = ut + 1/2 at² and v² - u² = 2as are valid only for uniformly accelerated motion.
• Do not use these equations blindly for circular motion or variable acceleration unless the question states uniform acceleration in a straight line.
• Initial velocity u is zero when a body starts from rest.
• Final velocity v is zero when a body comes to rest.
• Retardation means negative acceleration; write a as negative in calculations if direction is opposite.
• If the question says the object is moving with uniform velocity, acceleration is zero.
• If time is in minutes or hours, convert to seconds before substituting in SI-based formulas.

Exam tips and common mistakes

For 1-mark questions, definitions must include the reference point or direction wherever needed. For numericals, write the formula before substitution to secure method marks. Never confuse distance with displacement in round-trip questions. In graph questions, remember: slope of distance-time graph = speed, slope of velocity-time graph = acceleration, and area under velocity-time graph = displacement. Convert km/h to m/s using × 5/18 and m/s to km/h using × 18/5. If acceleration is negative, do not drop the minus sign; it shows retardation or opposite direction.

Quick revision checks

• Q: When can displacement be zero even if distance is not zero? A: When the object returns to its starting point, such as one complete round of a circular track.
• Q: What does the slope of a velocity-time graph represent? A: Acceleration.
• Q: A body moves with uniform velocity. What is its acceleration? A: Zero, because velocity does not change with time.
• Q: Which equation of motion should be used when time is not given? A: v² - u² = 2as.

Frequently Asked Questions