What is the average speed of an object that is moving at #22 m/s# at #t=0# and accelerates at a rate of #a(t) =t-8# on #t in [0,2]#?

1 Answer
Mar 17, 2018

Answer:

The average speed is #=3.67ms^-1#

Explanation:

#"Average speed " = "total distance travelled" /" time taken to cover that distance"#

The acceleration is

#a(t)=t-8#

The velocity is

#v(t)=inta(t)dt = int(t-8)dt = 1/2t^2-8t+C#

Plugging in the initial conditions

#v(0)=22ms^-1#

#22=0-0+C#

Therefore,

#v(t)=1/2t^2-8t+22#

The average speed is

#barv=1/(2-0)int_0^2(1/2t^2-8t+22)dt#

#=1/2[1/6t^3-4t^2+22t]_0^2#

#=1/2((1/6*8-16+22)-(0))#

#=3.67ms^-1#