Understanding Graphs of Motion

Graphs are very helpful in understanding laws of motion, but only if we understand those graphs. Different graphs of motion will be presented and explained. In this chapter we restrict these graphs to motion along a straight line, but graphs are used extensively in Physics

Parameters describing linear motion are:

D – displacement (sometimes denoted S),

v – velocity,

a – acceleration,

and they all may depend on time t.

All of the listed parameters may have initial value denoted usually by subscript 0:

D₀, v₀, a₀. 

Generally for any type of motion one can write

D = f₁(t)

v = f₂(t)

a = f₃(t)

We remind you the explicit forms of these functions for linear motion (along the straight line) with constant acceleration a.

 

D = D₀ + v₀t + at²/2                        (1)

v = v₀ + a t                                     (2)

 

In general case, when acceleration can depend on time,        

a(t) = a₀ + f(t)

and Eqs. 1 and 2 cannot be applied directly. Some examples of motion with varying acceleration will be given as Problems. These particular problems require some knowledge of calculus.

 

Links to different types of graphs are given below

Graph-1. Displacement versus time with constant velocity.

Graph-2. Velocity versus time, velocity constant

Email this article to friend