Plotting a graph of velocity of a body against time can be very useful when solving problems of linear motion.We are primarily interested in the graphs that involve a constant acceleration throughout or ones where the acceleration changes instantly from one value to another.
The slope of a velocity–time graph is equal to the acceleration. slope
y2 y1 x2 x1
v2 v1 t2 t1
v u t a
The area under the graph is equal to the distance travelled. area area of rectangle area of triangle
(base height) 1 2 (base height)
(t u) 1 2 (t (v u))
ut 1 2 t (u at u)
s ut 1
Linear motion 2 at2 Constant acceleration Increasing acceleration Decreasing acceleration
Time / s
Acceleration from rest, period of constant velocity, deceleration to rest
Time / s a > 0
Time / s a increasing Fig 2.19: Series of velocity–time graphs, showing different types of acceleration SCIENCE,TECHNOLOGY & SOCIETY
Athletics For a 100 m runner, there are three main phases to the race: the acceleration, max velocity and deceleration, as illustrated in the velocity–time graph below.
Time / s a decreasing
Fig 2.20:Velocity-time graph of a 100 m sprint race Time / s
