Forces & Motion

Speed

Speed is defined as a measure of the distance an object travels in a given length of time.

The average speed of an object can be determined from the equation below:

Thus, if a car travels 100 meters in 5 seconds its average speed can be calculated as;

Average speed = 100/5 = 20 meters per second

Average speed is used to give the speed of an object over a given interval of time, if however the speed of an object is required for a particular moment then the instantaneous speed is used.

Instantaneous speed is the speed of an object at a given moment. In this case the equation is similar to that of average speed but the time taken is a much smaller interval. A speedometer in the car gives an instantaneous speed as it gives the speed of the moving car at that specific time, whereas the average speed would be used as a measure of speed for the whole journey.

Velocity

Velocity is defined as a measure of the distance an object travels in a stated direction in a given length of time.

Thus velocity is speed in a stated direction. Velocity is referred to as a vector quantity because it possesses both size and direction, the size being speed. Where speed only tells us how fast or slow an object is moving it gives no reference of direction velocity is used as a more complete measure as it not only gives speed but also the direction.

Two cars could be travelling with the same speed of 100 km/h on a motorway. However, by stating one car is travelling 100 km/h north and the other 100 km/h south do we realise they are travelling in opposite directions, thus the velocity gives a better indication of the motion.

The average velocity of an object can be determined from the equation below:

Acceleration

For an object moving in a straight line where there is no change of direction the acceleration is defined as the rate of change of velocity with time.

It is given by the following equation.

Two cars could be travelling with the same speed of 100 km/h on a motorway. However, by stating one car is travelling 100 km/h north and the other 100 km/h south do we realise they are travelling in opposite directions, thus the velocity gives a better indication of the motion.

The average speed of an object can be determined from the equation below:

In the case where an object is slowing down (decreasing velocity) the acceleration is in the opposite direction to the moving object. This is referred to as negative acceleration or retardation or deceleration.

Distance-Time Graphs

Constructing graphs of an objects motion gives a better idea of the behaviour of the moving object.

A distance-time graph is constructed by having the distance as the vertical axis and the time as the horizontal axis. By recording the distance travelled over different intervals of time and plotting these values a distance-time graph can be plotted. From this plot information about the moving object can easily be extracted.

The animation below shows a distance-time graph:

Points to remember

In a distance-time graph;

• The average speed can be determined from the slope/gradient of the graph.
• The steeper the gradient the higher the average speed.
• A horizontal line indicates the object is stationary (not moving).
  

Velocity-Time Graphs

A velocity-time graph is constructed by having the velocity as the vertical axis and the time as the horizontal axis. By recording the velocity over different intervals of time and plotting these values a velocity-time graph can be plotted. From this plot information about the moving object can easily be extracted.

The animation below shows a velocity-time graph.

Points to remember

In a velocity-time graph:

• The acceleration can be determined from the slope/gradient of the graph. The steeper the gradient the higher the average speed.
• A horizontal line indicates the object is moving at constant velocity.
• The area under the graph gives the total distance travelled.