P2.1.1: Distance-Time Graphs
- 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
- 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.
- 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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