What is the average speed, on $t in [0,5]$ , of an object that is moving at $5 m/s$ at $t=0$ and accelerates at a rate of $a(t) =5-2t$ on $t in [0,4]$ ?

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Answer 1 · 2018-02-16T07:49:43

The average speed is $=9.53ms^-1$

The speed is the integral of the acceleration.

The acceleration is

$a(t)=5-2t$

The speed is

$v(t)=inta(t)dt=int(5-2t)dt$

$=5t-t^2+C$

Plugging in the initial conditions

$v(0)=5*0-0+C=5$

Therefore,

$v(t)=5t-t^2+5$

The speed when $t=4$ is

$v(4)=20-16+5=9ms^-1$

The average speed on the interval $[0,5]$ is

$barv*(5-0)=int_0^4(5t-t^2+5)dt+9*1$

$5barv=[5/2t^2-1/3t^3+5t]_0^4+9$

$5barv=(40-64/3+20)-(0)+9=116/3+9=47.67$

$barv=47.67/5=9.53ms^-1$

What is the average speed, on t in [0,5]t in [0,5], of an object that is moving at 5 m/s5 m/s at t=0t=0 and accelerates at a rate of a(t) =5-2ta(t) =5-2t on t in [0,4]t in [0,4]?