# Math Help - calculus/physics problem (graphing)

1. ## calculus/physics problem (graphing)

I am terrible at drawing graphs and don't know where to start with this.

A body has an equation of motion measured in metres after t seconds such that s=4/3t"3-14t"2+40t+8.

I need to draw three separate graphs, one for acceleration, velocity, and displacement and need to explain the relationship between the important info on the graph. ("s" in the equation is distance )

2. Originally Posted by math619
I am terrible at drawing graphs and don't know where to start with this.

A body has an equation of motion measured in metres after t seconds such that s=4/3t"3-14t"2+40t+8.

I need to draw three separate graphs, one for acceleration, velocity, and displacement and need to explain the relationship between the important info on the graph. ("s" in the equation is distance )

the displacement curve is a plot of:

$
s=4/3t^3-14t^2+40t+8
$

the velocity is the derivative of displacement:

$
v=\frac{ds}{dt}=4t^2-28t+40
$

and the acceleration is the derivative of velovity:

$
a=\frac{dv}{dt}=8t-28
$

The plots are attached

RonL