Graphs can help us describe and explain how an object moves-its motion.
A distance-time graph is an example of this. It compares the distance (which is on the y-axis) of an object from its starting point against the time taken (which is on the x-axis.)
The speed is the distance travelled per second, and is represented by the line on the distance-time graph.
The steeper the gradient of the line, the higher the speed is.
If the object isn't moving, then the line is horizontal on the graph.
If the object moves at a constant speed, then the line is a straight line sloping upwards.
Speed is calculated using the equation: Speed in m/s = distance travelled (m)÷time taken (s)
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P2.1.2: Velocity and Acceleration
Velocity is the speed in a given direction.
So if an object changes direction, its velocity changes even if the speed is the same. So, a car travelling north at 30m/s has the same speed as a car travelling south at 30m/s. However, their velocities are not the same because they are moving in opposite directions.
When the velocity changes, the object accelerates.
Acceleration is calculated using: a= v-u ÷ t
a= acceleration in m/s2.
v=final velocity in m/s
u=initial velocity in m/s
t=time taken for change in s
If the acceleration is negative, it means that it is decelerating.
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P2.1.3 Velocity-Time Graphs
A velocity-time graph shows the velocity (y-axis) against the time (x-axis).
The gradient (steepness) of the line represents the acceleration-the steeper the gradient, the greater the acceleration.
If the line is horizontal, then the accleration is 0, which does not mean that the object is stationery. It means that the object is moving at a constant speed.
When the gradient it negative, it is showing deceleration.
For example, braking on a vehicle reduces its velocity. This means that it is decelerating.
The area under the line on a velocity-time graph represents the distance travelled. The bigger the area under the line, the greater the distance travelled.
The actual calculated area under the line is equal to the distance travelled. For example, if the line is horizontal, and the object has a velocity of 30 m/s and the time is 5 seconds, the distance travelled would be 30x5 which is equal to 150m travelled.
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P2.1.4: Using Graphs
Distance-Time Graphs
Calculating the gradient of the line on this graph is working out the speed.
In order to work out the gradient, a triangle must be drawn under the line (just like working out the gradient of graphs in maths) and the hypotenuse (long, diagonal side of the triangle) must be a section of the original line.
Then, the height of the triangle must be divided by the base of the triangle in order to find the gradient-the speed in m/s.
If the line is curved, this means that the object is not moving at a constant speed.
Velocity-Time Graphs
The gradient of the line here is used to find the acceleration.
In order to find the acceleration the same steps for finding the gradient above must be taken, except the answer is in m/s2.
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