Kinematics
Contents
© The scientific sentence. 2010
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Physics: Kinematics
displacement
velocity
acceleration
graphs
1. Constant acceleration
When an object has an initial velocity vi and that is moving in a straight line with
constant acceleration a, the following equations connect the final velocity vf and displacement x in a given time t.
• vf = vi + a t
• x = (vi + vf)t/2
• x = vi t + (1/2) a t2
• x = vf t - (1/2) a t2
• vf2 = vi2 + 2 a x
Note: These equations cannot be used if the acceleration is not constant.
2. Variable acceleration
In the case that the acceleration is not constant, to determine a
variable such as timre (t), displacement (x), velocity (v) or acceleration (a)
from the anothers we use:
• The integral calculus, or
• The area under the curve of velocity or
acceleration with respect to time through a given graph.
Graphs can often be used to find displacement from velocity-time graph,
and velocity from acceleration-time graph.
This is due to:
• The gradient of a displacement-time graph is velocity: v = dx/dt, and
• The gradient of a velocity-time graph is acceleration: a = dv/dt.
 By using geometrical figures area formulas':
The area under a velocity-time graph
indicates the displacement .
The area under an acceleration-time graph
indicates the velocity .
3. Velocity from acceleration
4. Displacement from velocity
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