# What is the average speed of an object that is moving at 9 m/s at t=0 and accelerates at a rate of a(t) =5-2t on t in [0,5]?

Nov 8, 2016

Average speed is the mean of initial velocity and final velocity.

to solve this question we need to take out final velocity ($v$) and initial velocity($u$) is already proided.

so lets proceed.

$a \left(t\right) = 5 - 2 t$
therefore accereleration at 5 seconds is -5$\frac{m}{s} ^ 2$.This is derieved by puting t=5 in the above equation/function.

$a = \frac{v}{t} - \frac{u}{t}$

by putting values this we get $v = - 12 \frac{m}{s}$

so $u = 9 \frac{m}{s}$ and $v = - 12 \frac{m}{s}$

${V}_{a} v = \frac{u + v}{2}$
=$- 1.5 \frac{m}{s}$ .

I haven't showed the actual mathematics calculation as i hope you can easily make it,she see the procedure.