# What is exact change in position of the particle?

## The velocity of a particle moving along the x-axis is given by f(t)=15−5tcm/s. Use a graph of f(t) to find the exact change in position of the particle from time t=0 to t=4 seconds.

Nov 11, 2017

Change in position is also called displacement. It is a vector quantity.

#### Explanation:

Given $f \left(t\right) = 15 - 5 t$

at $t = 0$, $f = 15$
at $t = 1$, $f = 10$
at $t = 2$, $f = 5$
at $t = 3$, $f = 0$
at $t = 4$, $f = - 5$

Plot graph as below

$\text{Displacement"="Area under the curve for } t = 0 \to t = 4$

We know that $\text{Area of a triangle "=1/2xx"base"xx"height}$

$\therefore \text{Displacement"="Area of "Delta ABC+"Area of } \Delta C D E$
$\implies \text{Displacement} = \frac{1}{2} \times 3 \times 15 + \frac{1}{2} \times \left(- 5\right) \times 1$
$\implies \text{Displacement} = 22.5 - 2.5 = 20 c m$