Motion
Section: Physics | Syllabus: Cambridge IGCSE Combined Science (0653)
Speed
Speed tells us how fast an object is moving, it is defined as:
Distance covered per unit of time
- It is a scalar quantity
- has magnitude but no direction
- Formula:
-
v = (s/t)
- Where:
- v = speed (m/s)
- s = distance travelled (m)
- t = time taken (s)
- The equation can be rearranged to find distance or time:
- d = s × t
- t = (s/v)
Average Speed
- When speed varies during a journey, we use the average speed
- This gives the overall speed of the whole journey, even if the object was speeding up or slowing down along the way.
- Formula: Average Speed=(Distance Travelled/Time Taken)
Speed, distance and time formula triangle
How to use the triangles
- Cover the quantity you want to calculate with your finger.
- Look at the remaining two quantities.
- Quantities on the same line are multiplied.
- Quantities with one above the other are divided. Always divide the top quantity by the bottom quantity.
How to use the triangle formula to find speed, distance and time
Distance-Time Graphs
- A distance-time graph shows how the distance travelled by an object changes over time
- It can be used to:
- describe the motion of an object
- calculate the object's speed
Constant speed on a distance-time graph:
- On a distance-time graph:
- a straight line means the object is moving at a constant speed
- a horizontal line means the speed is zero (the object is stationary)
- a sloped straight line means the object is moving at a steady, non-zero speed
- the horizontal (x) axis represents time
- the vertical (y) axis represents distance
Distance-time graph showing a straight line moving away from the origin, representing an object travelling at constant speed
Gradient (slope) of a distance-time graph:
- The gradient (slope) of a distance-time graph represents the object's speed
- a steeper line(gradient) means greater speed
- a shallower line(gradient) means slower speed
Distance-time graph with two straight lines of different gradients, showing that a steeper line means a faster speed
- Both lines above show constant speeds, since both are straight
- the steeper line is the faster-moving object
- the shallower line is the slower-moving object
Changing speed on a distance-time graph
- If the speed of an object is changing, the object is accelerating or decelerating
- this shows up as a curved line, not a straight one
- a curve means the gradient itself is changing
- Reading the curve:
- gradient increasing over time → object speeding up (accelerating)
- gradient decreasing over time → object slowing down (decelerating)
Distance-time graph with two straight lines of different gradients, showing that a steeper line means a faster speed
- A curve with a decreasing gradient shows an object decelerating (slowing down)
- A curve with an increasing gradient shows an object accelerating (speeding up)
Working out speed from a distance-time graph
- Working out speed from the graph:
- speed = gradient of the line
- Formula:
-
speed = (Δ y/Δ x)
- Where:
- Δ y = change in distance (the y-axis values)
- Δ x = change in time (the x-axis values)
Distance-time graph showing how to find the gradient using change in y over change in x, to calculate speed
Speed-Time Graphs
- A speed-time graph describes how the speed of an object changes over a period of time.
- The gradient (slope) of the line represents the acceleration of the object:
- A positive gradient (sloping upwards) represents acceleration.
- A negative gradient (sloping downwards) represents deceleration (negative acceleration).
- Motion with constant speed or constant acceleration is represented by straight lines:
- A horizontal line along the x-axis means the object is stationary (v = 0).
- A horizontal line above the x-axis means the object is moving at a constant speed (acceleration = 0).
- A straight sloped line means the object is moving with constant acceleration or constant deceleration.
Speed-time graph showing a horizontal line for constant speed and straight sloped lines for constant acceleration and deceleration
- Motion with changing acceleration is represented by a curved line:
- A curve getting steeper shows an increasing acceleration over time.
- A curve getting flatter shows a decreasing acceleration over time.
Speed-time graph showing curved lines representing increasing and decreasing acceleration
Calculating Acceleration from a Speed–Time Graph
- Acceleration is defined as the rate of change of velocity
- To calculate acceleration, you need to find the gradient of the line in the section of the graph you are interested in:
- For a straight-line section (constant acceleration), the gradient is constant.
- For a curved section (changing acceleration), the gradient is changing, so you should find the gradient of the tangent to the curve at the point of interest.
- Formula:
- acceleration = gradient = (Δ y/Δ x)
- Where:
- Δ y = change in speed on the vertical y-axis (Δ v)
- Δ x = change in time on the horizontal x-axis (Δ t)
Speed-time graph showing how to find the gradient using change in y over change in x, to calculate acceleration
Calculating Distance Travelled
- The total distance travelled by an object is equal to the total area underneath its speed-time graph.
- For rectangular sections (constant speed): area = base × height
- For triangular sections (constant acceleration from rest, or to rest): area = (1/2) × base × height
Speed-time graph showing how to calculate the area under the curve, to determine distance travelled
- Some graphs combine a sloped section with a horizontal section, forming a
- Total Distance:
- Total Distance = Area of Rectangle + Area of Triangle = (base) + ((1/2))
Free Fall and the Acceleration of Free Fall
- When an object falls near the Earth's surface (ignoring air resistance), it accelerates downward due to gravity
- The acceleration of any object falling freely near the Earth's surface is approximately constant:
- g ≈ 9.8 m/s^2 (downward)
- This means every second an object falls freely, its downward speed increases by about 9.8 m/s
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