Understanding motion, speed, velocity, acceleration and equations of motion
Motion is the change in position of an object with respect to time and its surroundings. An object is said to be in motion if it changes its position with time.
Imagine you're sitting in a train. Are you moving or stationary? It depends! If you compare yourself to the train seat, you're not moving. But if you compare yourself to trees outside, you're moving fast! Motion is always relative - it depends on your reference point (frame of reference).
Rest: An object is at rest if it does not change its position with time.
Motion: An object is in motion if it changes its position with time.
Frame of Reference: A set of coordinates (or surroundings) with respect to which motion is described.
Everything is relative! An object can be at rest with respect to one frame and in motion with respect to another.
A passenger sitting in a moving bus:
• Is at rest with respect to other passengers (same frame)
• Is in motion with respect to trees on roadside (different frame)
• Is in motion with respect to the ground
So motion and rest are relative terms!
Motion along a straight line.
Examples: A car moving on a straight road, a ball falling vertically downward, an athlete running on a straight track.
Motion along a circular path.
Examples: Earth revolving around Sun, a stone tied to string and whirled in a circle, motion of fan blades.
Motion that repeats itself after regular intervals of time.
Examples: Motion of pendulum, motion of Earth around Sun (365 days), motion of hands of a clock.
Motion in which an object moves to and fro about a mean position.
Examples: Motion of pendulum, motion of a swing, vibration of guitar strings.
Distance is the total path length covered by an object during its motion. It is a scalar quantity (has only magnitude, no direction).
Displacement is the shortest distance between initial and final positions of an object. It is a vector quantity (has both magnitude and direction).
| Feature | Distance | Displacement |
|---|---|---|
| Type | Scalar (magnitude only) | Vector (magnitude + direction) |
| Definition | Total path length covered | Shortest distance from start to end |
| Value | Always positive | Can be positive, negative, or zero |
| Path Dependence | Depends on actual path | Independent of path |
| Magnitude Comparison | Distance ≥ Displacement | Displacement ≤ Distance |
A person walks 4 m East, then 3 m North:
Distance: Total path = 4 m + 3 m = 7 m
Displacement: Shortest distance from start to end
Using Pythagoras theorem: √(4² + 3²) = √(16 + 9) = √25 = 5 m
Direction: Northeast (at an angle)
Notice: Distance (7 m) > Displacement (5 m)
When an object moves along a straight line in one direction only, distance equals displacement.
Example: A car moves 100 m straight east.
Distance = 100 m
Displacement = 100 m east
But if the car returns to starting point:
Distance = 200 m (100 m + 100 m)
Displacement = 0 m (back at starting point!)
Speed is the distance traveled per unit time. It tells us how fast an object is moving. Speed is a scalar quantity.
Speed = Distance / Time
v = s / t
SI unit: meter per second (m/s)
Other units: km/h, cm/s
Average Speed = Total Distance Traveled / Total Time Taken
If an object travels distances s₁, s₂, s₃... in times t₁, t₂, t₃...
Average Speed = (s₁ + s₂ + s₃...) / (t₁ + t₂ + t₃...)
A car travels 150 km in 3 hours. Find its speed.
Solution:
Distance = 150 km
Time = 3 hours
Speed = Distance / Time = 150 / 3 = 50 km/h
The car travels at 50 km per hour.
Velocity is the displacement per unit time. It tells us how fast an object is moving in a particular direction. Velocity is a vector quantity.
Velocity = Displacement / Time
v = s / t
SI unit: meter per second (m/s)
Direction must be specified!
Average Velocity = Total Displacement / Total Time Taken
v_avg = (Final Position - Initial Position) / Total Time
| Feature | Speed | Velocity |
|---|---|---|
| Type | Scalar quantity | Vector quantity |
| Definition | Distance per unit time | Displacement per unit time |
| Direction | No direction specified | Direction must be specified |
| Value | Always positive | Can be positive or negative |
| Zero Condition | Only when object is at rest | Can be zero even when object is moving (if it returns to start) |
An athlete runs around a circular track of 400 m and completes one round in 50 seconds.
Speed:
Distance = 400 m (full circle)
Time = 50 s
Speed = 400/50 = 8 m/s
Velocity:
Displacement = 0 m (back at starting point)
Time = 50 s
Velocity = 0/50 = 0 m/s
The athlete has speed but zero velocity!
Acceleration is the rate of change of velocity. It measures how quickly velocity is changing with time. Acceleration is a vector quantity.
Acceleration = Change in Velocity / Time Taken
a = (v - u) / t
Where:
u = initial velocity
v = final velocity
t = time taken
SI unit: meter per second squared (m/s²)
1. Positive Acceleration: When velocity increases with time (speeding up)
Example: A car starting from rest
2. Negative Acceleration (Retardation/Deceleration): When velocity decreases with time (slowing down)
Example: A car applying brakes
3. Zero Acceleration: When velocity remains constant (uniform velocity)
Example: A car moving at constant speed
A car accelerates from 10 m/s to 30 m/s in 4 seconds. Find acceleration.
Solution:
Initial velocity (u) = 10 m/s
Final velocity (v) = 30 m/s
Time (t) = 4 s
Acceleration (a) = (v - u) / t
a = (30 - 10) / 4
a = 20 / 4
a = 5 m/s²
The car accelerates at 5 m/s² (velocity increases by 5 m/s every second).
Imagine you're driving a car:
• When you press the accelerator (gas pedal), you speed up → Positive acceleration
• When you press the brake, you slow down → Negative acceleration (retardation)
• When you maintain constant speed → Zero acceleration
• When you take a turn at constant speed → Still accelerating! (direction changes)
A graph showing how distance changes with time. Time is taken on X-axis and distance on Y-axis.
1. Straight horizontal line: Object at rest (no change in distance)
2. Straight sloping line: Uniform speed
• Steeper slope = Higher speed
• Gentle slope = Lower speed
3. Curved line: Non-uniform speed (acceleration)
• Curve getting steeper = Increasing speed
• Curve getting gentler = Decreasing speed
Slope of distance-time graph = Speed
Speed = Slope of distance-time graph
Speed = (Change in distance) / (Change in time)
Speed = (y₂ - y₁) / (x₂ - x₁)
A graph showing how velocity changes with time. Time is taken on X-axis and velocity on Y-axis.
1. Straight horizontal line: Uniform velocity (zero acceleration)
2. Straight sloping line: Uniform acceleration
• Upward slope = Positive acceleration (speeding up)
• Downward slope = Negative acceleration (slowing down)
• Steeper slope = Greater acceleration
3. Curved line: Non-uniform acceleration
Slope of velocity-time graph = Acceleration
Area under velocity-time graph = Displacement
Acceleration:
Acceleration = Slope of v-t graph
a = (v₂ - v₁) / (t₂ - t₁)
Displacement:
Displacement = Area under v-t graph