Homework SourseThe velocity of a particle is described by vt81t001t3 for 0
The velocity of a particle is described by v(t)=81t-0.01t^3 for 0<t<90, where t is measured in seconds and
v(t) is measured in feet per second.
a)Find the acceleration of the particle at t=60 seconds. Label
b)What is the average velocity of the particle over the indicated 90 second period of time.
Show your work
v(t) is measured in feet per second.
a)Find the acceleration of the particle at t=60 seconds. Label
b)What is the average velocity of the particle over the indicated 90 second period of time.
Show your work
Solution
a. v(t)=81t-0.01t^3
Then,
a(t)=81-3(0.01)t^2
And so,
a(60)=81-.03(60)^2=-27 feet/second^2
b.v(t)=81t-0.01t^3
Then,
s(t) = 81/2t^2 - 0.01/4 t^4
vavg = (s(60)-s(0))/(60-0)
= (81/2*60^2 - 0.01/4*60^4)/60
= 1890 feet/second
