A-Level Maths: Q2-01 [Kinematics: Displacement / Time Graphs]

TLMaths

3 chapters5 takeaways9 key terms5 questions

Overview

This video introduces displacement-time graphs and contrasts them with distance-time graphs, focusing on how to interpret them in kinematics. It explains that the gradient of a displacement-time graph represents velocity (which can be negative), while the gradient of a distance-time graph represents speed (always positive). The video uses a practical example of a person walking back and forth to illustrate these differences and how the graphs are constructed.

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Chapters

A displacement-time graph plots displacement (in meters) on the y-axis against time (in seconds) on the x-axis.
Displacement measures the change in position from a starting point, and can be positive or negative.
The graph can show movement in a positive direction (increasing displacement) and a negative direction (decreasing displacement).

Understanding displacement-time graphs is crucial for visualizing and analyzing an object's motion, especially when it changes direction.

A person walks 2 meters in the positive direction (reaching +2m displacement) in 5 seconds, then walks 7 meters back in the negative direction (reaching -5m displacement) over the next 10 seconds.

Distance-time graphs plot total distance traveled on the y-axis against time on the x-axis.
Distance is always positive, so a distance-time graph will never decrease.
When an object changes direction, its displacement-time graph may show a decrease, while its distance-time graph will continue to increase.

Distinguishing between distance and displacement is key to accurately describing motion, as they represent different physical quantities.

After walking 2m and then 7m back, the displacement is -5m, but the total distance traveled is 9m (2m + 7m).

The gradient of a displacement-time graph represents the object's velocity.
Velocity can be positive (moving away from the origin) or negative (moving towards the origin or in the opposite direction).
The gradient of a distance-time graph represents the object's speed.
Speed is always positive, reflecting the rate of change of distance traveled.

The gradient provides a direct measure of how fast an object is moving and in which direction, which is fundamental to kinematic analysis.

For the first 5 seconds, the gradient (velocity) is 2m/5s = 0.4 m/s. For the next 10 seconds, the gradient (velocity) is -7m/10s = -0.7 m/s, indicating movement in the opposite direction.

Key takeaways

1Displacement is a vector quantity measuring change in position from a reference point, while distance is a scalar quantity measuring the total path length.
2Displacement-time graphs can show negative gradients, indicating movement in the negative direction, whereas distance-time graphs only show positive gradients.
3The gradient of a displacement-time graph represents velocity, which can be positive, negative, or zero.
4The gradient of a distance-time graph represents speed, which is always non-negative.
5When an object reverses direction, its displacement decreases (or becomes more negative), but its total distance traveled continues to increase.

Key terms

DisplacementDistanceDisplacement-Time GraphDistance-Time GraphGradientVelocitySpeedKinematicsOrigin

Test your understanding

1What is the fundamental difference between displacement and distance?
2How does the gradient of a displacement-time graph relate to the motion of an object?
3Why does a distance-time graph never decrease, even if an object changes direction?
4What does a negative gradient on a displacement-time graph signify about the object's movement?
5How would you calculate the velocity of an object from a specific segment of a displacement-time graph?