# The velocity function is v(t)=-t^2+4t-3 for a particle moving along a line. Find the displacement of the particle during the time interval [0,5]?

Jul 26, 2015

The problem is illustrated below.

#### Explanation:

Here, the velocity of the particle is expressed as a function of time as,

$v \left(t\right) = - {t}^{2} + 4 t - 3$

If $r \left(t\right)$ is the displacement function, it is given as,

r(t) = int_(t""_0)^t v(t)*dt

According to the conditions of the problem, t""_0 = 0 and $t = 5$.

Thus, the expression becomes,

$r \left(t\right) = {\int}_{0}^{5} \left(- {t}^{2} + 4 t - 3\right) \cdot \mathrm{dt}$

$\implies r \left(t\right) = \left(- {t}^{3} / 3 + 2 {t}^{2} - 3 t\right)$ under the limits $\left[0 , 5\right]$

Thus, $r = - \frac{125}{3} + 50 - 15$
The units need to be put.