Question

Velocity of the partical changes with time in seconds as v=(t-4)m/s .average velocity of the partical in the interval (0-6)second is

Answer 1

Here velocity varies with time, so average velocity can be found by
$\bold{\ \textless \ v\ \textgreater \ =\frac{\int\linits^a_b{v(t)}\,dt}{\int\limits^a_bdt}}$
here is the average velocity of particle .

Now, < v > = $\bold{\ \textless \ v\ \textgreater \ =\frac{\int\linits^6_0{(t-4)},dt}{\int\limits^6_0dt}}$
= [t²/2 - 4t]⁶₀/[t]⁶₀
= [36/2 - 24]/[6]
= (18 - 24)/6
= -6/6
= -1

Hence, average velocity = -1 m/s