What is the average speed of an object that is moving at 22 m/s22ms at t=0t=0 and accelerates at a rate of a(t) =t-8a(t)=t−8 on t in [0,2]t∈[0,2]?

1 Answer
Narad T.
Mar 17, 2018

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

Explanation:

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

The acceleration is

a(t)=t-8a(t)=t−8

The velocity is

v(t)=inta(t)dt = int(t-8)dt = 1/2t^2-8t+Cv(t)=∫a(t)dt=∫(t−8)dt=12t2−8t+C

Plugging in the initial conditions

v(0)=22ms^-1v(0)=22ms−1

22=0-0+C22=0−0+C

Therefore,

v(t)=1/2t^2-8t+22v(t)=12t2−8t+22

The average speed is

barv=1/(2-0)int_0^2(1/2t^2-8t+22)dt¯v=12−0∫20(12t2−8t+22)dt

=1/2[1/6t^3-4t^2+22t]_0^2=12[16t3−4t2+22t]20

=1/2((1/6*8-16+22)-(0))=12((16⋅8−16+22)−(0))

=3.67ms^-1=3.67ms−1

Related questions
See all questions in Acceleration
Impact of this question
1437 views around the world
You can reuse this answer
Creative Commons License