A Classical Approach of Newtonian Mechanics

2 MOTION IN 1 DIMENSION 2.6 Motion with constant acceleration

dx

x

x 0

0

0 t^

v ^ v^

v 0 ^ t^

0

0 t^

Figure 8: Graphs of displacement versus time and velocity versus time for a body moving with con-

stant acceleration

This line can be represented algebraically as

x = x 0 + v 0

t +

1

a t^2. (2.9)

2

Here, x 0 is the displacement at time t = 0: this quantity can be determined from

the graph as the intercept of the curved-line with the x-axis. Likewise, v 0 is the

body’s instantaneous velocity at time t = 0.

The velocity-time graph consists of a straight-line which can be represented

algebraically as

v = = v 0 + a t. (2.10)

dt