# Motion and Displacement-Time Graphs — IB Physics
Kinematics describes motion without worrying about its causes. In IB Physics, you must distinguish between scalar and vector quantities and fluently interpret motion graphs.
1. Scalars and Vectors
| Scalar | Vector |
|---|---|
| Distance | Displacement |
| Speed | Velocity |
| (no scalar) | Acceleration |
Distance = total path length; Displacement = straight-line distance from start to finish with direction.
Speed = distance/time; Velocity = displacement/time.
2. Displacement-Time ($s$-$t$) Graphs
- Gradient = velocity
- Straight line = constant velocity
- Curved line = changing velocity (acceleration)
- Horizontal line = stationary
- Negative displacement = opposite direction
3. Velocity-Time ($v$-$t$) Graphs
- Gradient = acceleration
- Area under curve = displacement
- Horizontal line = constant velocity (zero acceleration)
- Straight sloping line = constant acceleration
- Line crossing zero = change in direction
4. Acceleration-Time ($a$-$t$) Graphs
- Area under curve = change in velocity
- Horizontal line = constant acceleration (uniformly accelerated motion)
5. Instantaneous vs Average
- Average velocity = total displacement / total time
- Instantaneous velocity = gradient of - graph at a point (tangent)
- Average acceleration =
- Instantaneous acceleration = gradient of - graph at a point
Worked Example: Example 1
Problem
A car travels 300 m East and then 100 m West in 20 s.
Distance = 400 m. Speed = 400/20 = 20 m/s. Displacement = 200 m East. Velocity = 200/20 = 10 m/s East.
Solution
Worked Example: Example 2
Problem
From a - graph: velocity goes from 0 to 15 m/s in 5 s, then stays at 15 m/s for 10 s.
m/s² Displacement = area = m
Solution
7. IB Exam Tips
- Always include units and direction for vectors
- Tangent lines for instantaneous quantities
- Be careful with the sign of displacement
- Area under - can be negative (displacement in opposite direction)
8. Practice Questions
- Distinguish between distance and displacement. (2 marks)
- A ball is thrown up and returns to the thrower in 4 s. The maximum height is 20 m. Find (a) distance, (b) displacement, (c) average speed, (d) average velocity. (4 marks)
- Sketch the - graph for an object that decelerates uniformly from 20 m/s to rest in 8 s. Calculate the displacement. (3 marks)
Answers
- Distance is the total path length (scalar). Displacement is the straight-line distance from start to finish in a specified direction (vector).
- (a) 40 m (b) 0 m (c) 40/4 = 10 m/s (d) 0/4 = 0 m/s.
Want to check your answers and get step-by-step solutions?
Summary
- - gradient = velocity; - gradient = acceleration; - area = displacement
- Instantaneous values = tangent gradient
- Vectors have magnitude AND direction