Science GCSE
PHYSICS
Motion
Displacement, velocity, acceleration and force are all vector quantities. The speed of an object can be calculated from the slope on a distance-time graph.
The velocity of an object is its speed in a particular direction. The slope on a velocity-time graph represents the acceleration of an object. The distance travelled is equal to the area under a velocity-time graph.
Forces and motion
At Key Stage 3, you learned to calculate the speed of an object using the time taken and the distance travelled. At GCSE we take this knowledge further to look at vector quantities. A vector quantity has a size and a direction. The following are all vector quantities:
- Displacement
- Velocity
- Acceleration
- Force
Displacement
Displacement is the distance travelled in a straight line. It has both a direction and a size.
Velocity
The velocity of an object is its speed in one particular direction.
Acceleration
The acceleration of an object is calculated from its change in velocity and the time taken.
The force of an object is also a vector as it has a size (measured in Newtons) and a direction.
Speed
Speed, distance and time
At Key Stage 3, you learned how to calculate the speed of an object from the distance travelled and the time taken.
The equation
When an object moves in a straight line at a steady speed, you can calculate its speed if you know how far it travels and how long it takes. This equation shows the relationship between speed, distance travelled and time taken:
- For example, a car travels 300 metres in 20 seconds.
- Its speed is 300 ÷ 20 = 15m/s.
The speed of an object can then be used to calculate the velocity.
Check your understanding of this topic by trying this activity.
Distance-time graphs
You should be able to draw and explain distance-time graphs for objects moving at steady speeds or standing still.
Background information
The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start.
Features of the graphs
When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed, the line on the graph is straight, but sloped.
The diagram shows some typical lines on a distance-time graph.
Note that the steeper the line, the greater the speed of the object. The blue line is steeper than the red because it represents an object moving faster than the one represented by the red line.
The red lines on the graph represent a typical journey where an object returns to the start again. Notice that the line representing the return journey slopes downwards.
Velocity-time graphs
You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration.
Acceleration: The rate of change of velocity, measured in metres per second squared.
Acceleration = change of velocity divided by time taken.
Background information
The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities.
The vertical axis of a velocity-time graph is the velocity of the object. The horizontal axis is the time from the start.
Features of the graphs
When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a constant acceleration, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph.
The steeper the line, the greater the acceleration of the object. The blue line is steeper than the red line because it represents an object with a greater acceleration.
Notice that a line sloping downwards - with a negative gradient - represents an object with a constant deceleration - slowing down.
Calculating distance - Higher tier
The distance travelled can be calculated from the graph, too. The area under the graph is equal to the distance travelled. Study this velocity-time graph.
- Question
- What is the acceleration represented by the sloping line?
- Answer
- The object increases its velocity from 0m/s to 8m/s in 4 s.
- Its acceleration is 8 ÷ 4 = 2 m/s2.
The area
The area under the line in a velocity-time graph represents the distance travelled. To find the distance travelled in the graph above, you need to find the area of the light-blue triangle and the dark-blue rectangle.
- Area of light-blue triangle
- The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation:
- area of triangle = 1⁄2 × base × height
- so the area of the light-blue triangle is 1⁄2 × 8 × 4 = 16 m
- Area of dark-blue rectangle
- The width of the rectangle is 6 seconds and the height is 8 metres per second. So the area is 8 × 6 = 48 m.
- Area under the whole graph
- The area of the light-blue triangle plus the area of the dark-blue rectangle is:
- 16 + 48 = 64 m.
- This is the total area under the distance-time graph. This area represents the distance covered.
Acceleration
You should be able to calculate the acceleration.
Acceleration:The rate of change of velocity, measured in metres per second squared.
The formula:
Acceleration = change of velocity divided by time taken. of an object from its change in velocity and the time taken.
The equation
When an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. This equation shows the relationship between acceleration, change in velocity and time taken:
- For example, a car accelerates in 5s from 25 m/s to 35 m/s.
- Its velocity changes by 35 - 25 = 10 m/s.
- So its acceleration is 10 ÷ 5 = 2 m/s2.
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