# Kinematics## Velocity - Time Graph
Sometimes it is useful in solving problems in kinematics if a velcoity - time graph is drawn first.
For example, if a body accelerates uniformly from rest, then travels at a constant velocity v before retarding uniformly to rest again the graph (fig:1)will take the folowing shape:
Fig:1 |
*Note: The section numbers below relate to those of the graph above.*
**Section 1**
acceleration is given by:
Therefore (since u = 0)
The slope of the graph = acceleration
Simimlarly for distance travelled:
Therefore
Distance travelled is given by the area under the graph for section 1.
**Section 2**
Distance travelled: which again is the area under the graph for this section.
**Section 3**
As in sections 1. and 2. the distance travelled is given by the area under the graph for this
section, i.e.
The acceleration is given by: i.e. the slope of the graph.
Note that this time the slope of the graph and acceleration are negative because the body is slowing down. |