Everything Science Grade 10

CHAPTER 21. MOTION IN ONE DIMENSION 21.6

Velocity from acceleration vs. time graphs

Just as we used velocity vs. time graphs to find displacement, we can use acceleration vs.
time graphs to find the velocity of an object at a given moment in time. We simply calculate
the area under the acceleration vs. time graph, at a given time. In the graph below, showing
an object at a constant positive acceleration, the increase in velocity of the object after 2
seconds corresponds to the shaded portion.

v=area of rectangle=a×∆t

= 5m·s−^2 × 2 s

= 10m·s−^1

The velocity of the object att= 2s is therefore 10 m·s−^1.

Summary of Graphs ESAHE

The relation between graphs of position, velocity and acceleration as functions of time is
summarised in the next figure.

Stationary

object

x(m)

t(s)

v(m·s−^1 )

t(s)

a(m·s−^2 )

t(s)

Uniform

motion

x(m)

t(s)

v(m·s−^1 )

t(s)

a(m·s−^2 )

t(s)

Motion

with con-

stant accel-

eration

x(m)

t(s)

v(m·s−^1 )

t(s)

a(m·s−^2 )

t(s)

Figure 21.3: Position-time, velocity-time and acceleration-time graphs.

Physics: Mechanics 415