DISTANCE & DISPLACEMENT, SPEED, VELOCITY AND ACCELERATION
1. Distance
1.1 Definition
- Distance is the total length of the path travelled by an object, regardless of direction.
- Distance is a scalar quantity, which means it has magnitude only and no direction.
- Distance is always positive.
- The SI unit of distance is meter (m).
1.2 Example 1
- A car travels 10 km east and then 4 km west.
- Distance = 10 + 4 = 14 km
- Distance counts the total path travelled.
1.3 Example 2
- A student walks 5 m north and then 5 m south.
- Distance = 5 + 5 = 10 m
2. Displacement
2.1 Definition
- Displacement is the shortest straight-line distance from the starting point to the ending point, including direction.
- Displacement is a vector quantity, which means it has both magnitude and direction.
- Displacement can be positive, negative, or zero depending on direction.
- The SI unit of displacement is meter (m).
2.2 Example 1
- A car travels 10 km east and then 4 km west.
- Net movement = 10 − 4 = 6 km east
- Displacement = 6 km east
2.3 Example 2
- A student walks 5 m north and 5 m south.
- The final position is the starting point.
- Displacement = 0 m
2.4 Quick Difference Between Distance and Displacement
| Distance | Displacement |
| Distance is the total path travelled by an object. | Displacement is the shortest straight-line distance from start to end point. |
| It has no direction. | It has direction. |
| It is a scalar quantity (only magnitude). | It is a vector quantity (magnitude + direction). |
| It is always positive. | It can be positive, negative, or zero. |
| It depends on the actual path taken. | It depends only on the initial and final position. |
3. Explanation of Distance and Displacement in Circular Path
3.1 Concept
- If a body moves in a circle and returns to its starting point, the distance travelled and the displacement are different.
- When an object moves along a circular path, it follows the curved boundary of the circle.
- The length of this curved path is the distance travelled.
- If the object completes one full circle, the distance travelled is equal to the circumference of the circle.
Distance = 2πr
- where r is the radius of the circle.
- Since the object has moved along a path, the distance is not zero.
- It has actually covered a measurable length.
- However, displacement depends only on the initial and final positions.
- If the object returns to its starting point, the initial and final positions are the same.
- Therefore, the shortest straight-line distance between them is zero.
Displacement = 0
3.2 Example
- Suppose a runner runs once around a circular track of radius 7 m and comes back to the starting point.
Distance travelled = 2πr
= 2 × π × 7
= 14π m
≈ 44 m
Displacement = 0 m
3.3 Conclusion
- Distance depends on the actual path travelled.
- Displacement depends only on the change in position.
- When a body moves in a circle and returns to its starting point, the distance is not zero, but the displacement is zero.
- Speed
4.1. Definition
- Speed is the rate at which distance is covered.
- It tells us how fast an object is moving.
- Speed is a scalar quantity (it has magnitude only, no direction).
- SI unit of speed is meter per second (m/s).
4. 2. Formula
4.3 Example
- A car travels 100 meters in 5 seconds.
This means the car covers 20 meters every second.
- Velocity
5.1. Definition
- Velocity is the rate at which displacement changes.
- It tells us how fast an object is moving and in which direction.
- Velocity is a vector quantity (it has both magnitude and direction).
- SI unit of velocity is meter per second (m/s).
5.2. Formula
5.3. Example
- A car moves 50 meters east in 10 seconds.
Here, direction (east) is important.
- Key Difference
- Speed has no direction; velocity has direction.
- Speed depends on distance; velocity depends on displacement.
- Speed is scalar; velocity is vector.
- Problems:
- A car travels 100 m in 5 s
- Convert 72 km/h to m/s
- A runner runs 200 m in 25 s
- Average speed formula
- Object returns to starting point
Velocity = 0 (if total displacement 0)
- Can speed be negative?
❌ No
Velocity can be negative.
- ACCELERATION
- Define acceleration
Rate of change of velocity.
- Formula of acceleration
- A car increases speed from 10 m/s to 30 m/s in 5 s
- If velocity decreases from 20 to 10 m/s in 5 s
(Negative acceleration / Deceleration)
- Acceleration due to gravity
7.VELOCITY–TIME GRAPH
The gradient (slope) of a velocity–time graph represents acceleration.
Why?
The gradient of any graph is:
Gradient = Change in vertical axis / Change in horizontal axis
For a velocity–time graph:
Gradient = Change in velocity / Time
But,
Change in velocity / Time = Acceleration
Different Situations
1️. Positive Gradient
• Velocity increases with time
• Object is accelerating
• Acceleration is positive
2️. Negative Gradient
• Velocity decreases with time
• Object is decelerating (retarding)
• Acceleration is negative
3️. Zero Gradient (Horizontal Line)
• Velocity is constant
• Acceleration is zero
4️. Curved Line
• Acceleration is changing
• Gradient is different at different points
Final Statement
The gradient of a velocity–time graph represents the acceleration of the object.
8.Area Under Velocity -Time graph
✅ Answer:
The area under a velocity–time graph represents the displacement of the object.
🔎 Why?
On a velocity–time graph:
• Vertical axis (Y-axis) = Velocity
• Horizontal axis (X-axis) = Time
Area = base × height
Area = Velocity × Time
Velocity × Time = Displacement
Area under the graph = Displacement
Graphical Explanation
1️. Rectangle Shape (Constant Velocity)
If velocity is constant:
Area = v × t
This gives displacement directly.
2️. Triangle Shape (Uniform Acceleration)
If velocity increases uniformly:
Area = 1/2 × base × height
This gives displacement during acceleration.
3️. Irregular Shape (Changing Velocity)
• Divide into rectangles/triangles
• Add all areas
• Total area = Total displacement
⚠ Important Note
• Area above time axis → Positive displacement
• Area below time axis → Negative displacement
• Total displacement = (Area above axis) – (Area below axis)
Final Statement (Exam Ready)
The area under a velocity–time graph represents the displacement of the object.
3. An object moves at constant velocity 20 m/s for 5 s. Find distance.
Answer: 100 m
4. A velocity–time graph is a straight line rising from 0 to 40 m/s in 5 s. Find acceleration.
Answer: 8 m/s²
5. A car slows from 30 m/s to 10 m/s in 4 s. Find acceleration.
Negative means deceleration.
6. If velocity is constant, what is acceleration?
Acceleration = 0
Because slope = 0.
7. An object moves with velocity increasing non-uniformly. What does this mean?
It means:
- Acceleration is changing
- Graph is curved
- Acceleration is not constant
8. How can you tell from v–t graph that object is at rest?
Velocity = 0
Graph lies on time axis.
9. A triangular v–t graph has base 6 s and height 30 m/s. Find distance.
10. Why is a negative slope called retardation?
Because velocity decreases with time.
So acceleration is negative.
9.DISPLACEMENT–TIME GRAPH
Answer:
The gradient (slope) of a displacement–time graph represents the velocity of the object.
Why?
On a displacement–time graph:
• Vertical axis (Y-axis) = Displacement (d)
• Horizontal axis (X-axis) = Time (t)
Gradient = Δd / Δt=Velocity
Therefore, the slope of a displacement–time graph gives velocity.
Graphical Explanation
1️. Steep Slope (High Velocity)
• Large change in displacement in short time
• Large gradient
• Object moves fast
2️. Gentle Slope (Low Velocity)
• Small change in displacement
• Small gradient
• Object moves slowly
3️. Horizontal Line (Zero Velocity)
• No change in displacement
• Gradient = 0
• Object is at rest
4️. Curved Line (Changing Velocity)
• Velocity is changing
• Draw a tangent at a point
• Gradient of tangent = instantaneous velocity
⚠ Important Note
• Upward slope → Positive velocity
• Downward slope → Negative velocity
• Steeper line → Greater speed
Final Statement (Exam Ready)
The gradient of a displacement–time graph represents the velocity of the object.
12. What does a straight line in s–t graph mean?
Uniform velocity (constant velocity).
13. What does horizontal line in s–t graph mean?
Displacement not changing → object is at rest.
14. If s–t graph slopes downward, what does it mean?
Velocity is negative → object moving in opposite direction.
15. If slope becomes steeper with time, what does it mean?
Velocity increasing → acceleration present.
16. If slope becomes less steep with time?
Velocity decreasing → deceleration.
17. An object moves 60 m in 3 s. Find velocity.
18. If displacement is constant for 5 s, what is velocity?
Velocity = 0
Because displacement not changing.
ACCELERATION (6 Questions)
20. A bus starts from rest and reaches 20 m/s in 10 s. Find acceleration.
21. A car moving at 25 m/s stops in 5 s. Find acceleration.
22. Can an object accelerate at constant speed?
Yes, if direction changes (e.g., circular motion).
Because velocity changes (direction changes).
24. What does zero acceleration mean?
Velocity constant (speed and direction constant).
Definition
Terminal velocity is the maximum constant speed reached by a falling object when the force of gravity is balanced by air resistance.
Why Does It Happen?
When an object falls:
1. Gravity (Weight) pulls it downward.
2. Air resistance (Drag) pushes upward against the motion.
At first:
• Gravity > Air resistance
• The object accelerates (speed increases).
After some time:
• Air resistance increases as speed increases.
• Eventually, Air resistance = Gravity.
At this point:
• Net force = 0
• Acceleration = 0
• The object falls at a constant speed → This speed is called terminal velocity.
In Simple Words
Terminal velocity is the speed at which a falling object stops speeding up and continues falling at the same speed.
Important Points
• It depends on:
o Mass of the object
o Surface area
o Shape
o Air density
• A heavier object usually has a higher terminal velocity.
• A parachute increases surface area → increases air resistance → reduces terminal velocity.
Example
• A skydiver without a parachute: about 53 m/s (around 190 km/h).
• With parachute open: about 5–6 m/s (safe landing speed).
26. Why does a feather fall slower than a stone?
Because:
- Large surface area
- Large air resistance
- Reaches terminal velocity quickly
27. When object just starts falling, what is acceleration?
Approximately equal to gravity g≈10m/s2
28. What happens to acceleration as object approaches terminal velocity?
Acceleration decreases
Finally becomes zero.
29. Why does parachutist slow down when parachute opens?
Air resistance suddenly increases
Upward force > weight
Large deceleration occurs.
30. After parachute opens and stabilizes, what happens?
New smaller terminal velocity reached
Acceleration becomes zero again.
