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Physics

Representing motion

The slope on a distance-time graph represents the speed of an object. The velocity of an object is its speed in a particular direction. The slope on a velocity-time graph represents the velocity of an object. The distance travelled is equal to the area under a velocity-time graph

For example, a car travels 300m in 20s. Its speed is 300 ÷ 20 = 15m/s. Distance-time graphs You should be able to draw and explain distance-time graphs for objects moving at steady speeds or standing still. Background information The vertical axis of a distance-time graph is the distance travelled from the start, and the horizontal axis is the time from the start. Features of the graphs When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed, the line on the graph is straight, but sloped. The diagram shows some typical lines on a distance-time graph.

Velocity-time graphs You should be able to explain velocity-time graphs for objects moving with a constant velocity or a constant acceleration. Background information The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities. The vertical axis of a velocity-time graph is the velocity of the object and the horizontal axis is the time from the start. Features of the graphs When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a constant acceleration, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph.

The steeper the line, the greater the acceleration of

the object. The blue line is steeper than the red line

because it represents an object with a greater

acceleration than the one represented by the red line.

Notice that a line sloping downwards (with a negative

gradient) represents an object with a constant

deceleration (slowing down).

Distance-time graphs (Higher Tier) You should be able to calculate gradients on distance-time graphs. Background To calculate the gradient of the line on a graph, divide the change in the vertical axis by the change in the horizontal axis.

Velocity-time graphs (Higher Tier) You should be able to calculate gradients of velocity-time graphs and the areas under the graphs.

The area The area under the line in a velocity-time graph represents the distance travelled. To find the the distance travelled in the graph above we need to find the area of the light blue triangle and the dark blue square Step 1 - Area of light blue triangle The width of the triangle is 4 seconds and the height is 8 metres per second. To find area you use the equation: area of triangle = 1/2 x base x height so the area of the light blue triangle is 1/2 x 8 x 4 = 16m. Step 2 - Area of dark blue rectangle The width of the rectangle is 6 seconds and the height is 8 metres per second so the area is 8 x 6 = 48m. Step 3 - Area under the whole graph The area of the light blue triangle plus the area of the dark blue rectangle is: 16 + 48 = 64m. This is the total area under the distance time graph and this area represents the distance covered. To summarise: the gradient of a velocity time graph represents the acceleration the area under a velocity time graph represents the distance covered

Check your understanding of this by having a go at the following activity.

Resultant force You should be able to use the idea of the resultant force on an object to determine its movement. The resultant force An object may have several different forces acting on it. They can have different strengths and directions. But they can be added together to give the resultant force. This is a single force that has the same effect on the object as all the individual forces acting together. When the resultant force is zero When all the forces are balanced, the resultant force is zero. In this case: A stationary object remains stationary. A moving object keeps on moving at the same speed in the same direction. For example, in the diagram of the weightlifter, the resultant force on the bar is zero, so the bar does not move. Its weight acting downwards is balanced by the upward force provided by the weightlifter.

The longer the arrow, the bigger the force. In this diagram, the arrows are the same length, so we know they are the same size.