# #

The figure below shows a plot of velocity versus time for a particle moving with constant acceleration $$a_c$$. The particle has velocity $$v_0$$ at time $$t_0$$. In the time elapsed between $$t_0$$ and a later time $$t$$ ($$t > t_0$$), the particle is displaced $$\Delta x$$.

## Part 1#

Use this plot to derive an expression for $$\Delta x$$ in terms $$a_c$$, $$v_0$$, $$t_0$$, and $$t$$.

Note that it may not be necessary to use every variable. Use the following table as a reference for using each variable:

$$Variable$$

Use

$$a_c$$

a_c

$$v_0$$

v_0

$$t_0$$

t_0

$$t$$

t

## Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.