The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.
If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the accelerationThe rate of change in speed (or velocity) is measured in metres per second squared. Acceleration = change of velocity 梅 time taken. of the object.
The table shows what each section of the graph represents:
Section of graph
Gradient
Velocity
Acceleration
A
Positive
Increasing
Positive
B
Zero
Constant
Zero
C
Negative
Decreasing
Negative
D (v = 0)
Zero
Stationary (at rest)
Zero
Section of graph
A
Gradient
Positive
Velocity
Increasing
Acceleration
Positive
Section of graph
B
Gradient
Zero
Velocity
Constant
Acceleration
Zero
Section of graph
C
Gradient
Negative
Velocity
Decreasing
Acceleration
Negative
Section of graph
D (v = 0)
Gradient
Zero
Velocity
Stationary (at rest)
Acceleration
Zero
Calculating displacement - higher
The area under the graph can be calculated by:
using geometry (if the lines are straight)
counting the squares beneath the line (particularly if the lines are curved)
Example
Calculate the total displacement of the object, whose motion is represented by the velocity-time graph below.
Here, the displacement can be found by calculating the total area of the shaded sections below the line.
Find the area of the triangle:
\(\frac{1}{2} \times base \times height\)
\(\frac{1}{2} \times 4 \times 8 = 16\)
The area of the triangle is 16 m2
Find the area of the rectangle:
base 脳 height
(10 - 4) 脳 8 = 48
The area of the rectangle is 48 m2
Add the areas together to find the total displacement: