What is the average speed of an object that is not moving at $t=0$ and accelerates at a rate of $a(t) =5t-10$ on $t in [3, 5]$ ?

Question

1435 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-11T21:11:23

$v_a=51.25 m/s$

$(d v)/(d t)=a(t)$

$d v=a(t)*d t$

$int d v=int a(t) *d t$

$v=int(5t-10) *d t$

$v=5*t^2/2-10*t+C$

$t=0 rarr v=0 rarrc=0$

$v=5/2 t^2-10t$

$v_a=1/(5-3)int_3^5 |(5/2 t^2-10t)|d t$

$v_a=1/2[|5/2*t^3/3-10*t^2/2|_3^5]$

$v_a=1/2[(5/2*5^3/3-5*5^2)-(5/2*3^3/3-5*3^2)]$

$v_a=1/2[(625/6-125)-(45/2-45)]$

$v_a=1/2[(625-750)-(-45/2)]$

$v_a=1/2[-125+45/2]$

$v_a=|-51.25 |$

$v_a=51.25 m/s$

What is the average speed of an object that is not moving at t=0t=0 and accelerates at a rate of a(t) =5t-10a(t) =5t-10 on t in [3, 5]t in [3, 5]?