Interpret velocity-time graph for constant direction and understand significance of area under velocity-time graph.

VELOCITY-TIME GRAPH FOR CONSTANT DIRECTION:

When an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a steadily increasing velocity, or a steadily decreasing velocity, 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 more rapidly the velocity of the object is changing. The blue line is steeper than the red line because it represents an object that is increasing in velocity much more quickly than the one represented by the red line.

Notice that the part of the red line between 7 and 10 seconds is a line sloping downwards (with a negative gradient). This represents an object that is steadily slowing down.

AREA UNDER VELOCITY-TIME GRAPH:

            Study this velocity-time graph.

The area under the line in a velocity-time graph represents the distance travelled. To find the distance travelled in the graph above, we need to find the area of the light-gray triangle and the dark-gray rectangle.

1.    Area of light-gray triangle

o    The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation:

o    area of triangle = ¹⁄₂ × base × height

o    so the area of the light-gray triangle is ¹⁄₂ × 8 × 4 = 16 m.

2.    Area of dark-gray rectangle

o    The width of the rectangle is 6 seconds and the height is 8 metres per second. So the area is 8 × 6 = 48 m.

3.    Area under the whole graph

o    The area of the light-gray triangle plus the area of the dark-gray rectangle is:

o    16 + 48 = 64 m

o    This is the total area under the distance-time graph. This area represents the distance covered.

Summary

·         The gradient of a velocity-time graph represents the acceleration

The area under a velocity-time graph represents the distance covered