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Shape and Space
Statistics and Probability
Speed, Distance and Time
The following is a basic but important formula which applies when speed is constant (in other words the speed doesn't change):
Remember, when using any formula, the units must all be consistent. For example speed could be measured in m/s, distance in metres and time in seconds.
If speed does change, the average (mean) speed can be calculated:
In calculations, units must be consistent, so if the units in the question are
not all the same (e.g. m/s, m and s or km/h, km and h), change the units before
starting, as above.
Change 15km/h into m/s.
If a car travels at a speed of 10m/s for 3 minutes, how far will it travel?
Velocity and Acceleration
Velocity is the speed of a particle and its direction of motion
(therefore velocity is a vector quantity, whereas
speed is a scalar quantity).
A car starts from rest and within 10 seconds is travelling at 10m/s. What is its acceleration?
These have the distance from a certain point on the vertical axis and the time on the horizontal axis. The velocity can be calculated by finding the gradient of the graph. If the graph is curved, this can be done by drawing a chord and finding its gradient (this will give average velocity) or by finding the gradient of a tangent to the graph (this will give the velocity at the instant where the tangent is drawn).
Velocity-Time Graphs/ Speed-Time Graphs
A velocity-time graph has the velocity or speed of an object on the vertical axis and time on the horizontal axis. The distance travelled can be calculated by finding the area under a velocity-time graph. If the graph is curved, there are a number of ways of estimating the area (see trapezium rule below). Acceleration is the gradient of a velocity-time graph and on curves can be calculated using chords or tangents, as above.
The distance travelled is the area under the graph.
On travel graphs, time always goes on the horizontal axis (because it is the independent variable).
This is a useful method of estimating the area under a graph. You often need to find the area under a velocity-time graph since this is the distance travelled.
Area under a curved graph = ˝ × d × (first + last + 2(sum of rest))
d is the distance between the values from where you will
take your readings. In the above example, d = 1. Every 1 unit on the horizontal
axis, we draw a line to the graph and across to the y axis.