(1)s=(1/3)t^3−5t^2+25t+3Accelerationattimet=?(2)Aparticlemovesalongastraightlineanditspositionattimetisgivenbys(t)=t^4−6t+18,t≥0.wheresismeasuredinfeetandtinseconds.Findthetotaldistance?trav

Question

(1)s=(1/3)t^3−5t^2+25t+3
Acceleration at time t =_____?
(2)A particle moves along a straight line and its position at time t is given by s(t)=t^4−6t+18,t≥0.where s is measured in feet and t in seconds.
Find the total distance________?traveled during the first 8 seconds.
(3) If a ball is thrown vertically upward from the roof of 32 foot building with a velocity of 16ft/sec,its height after t seconds is s(t)=32+16t−16t^2.
What is the velocity of the ball when it hits the ground (height 0)?
(4)A spherical balloon is being inflated.Find the rate of increase (with respect to the radius r) of the surface area (S=4πr^2) when:
r=2 inches → Rate of increase =______?
r=3 inches → Rate of increase =______?
r=6 inches → Rate of increase =______?

Answer 1

(1)2t-10
(2)当t=(3/2)的开三次方时速度为零,之前物体是向反方向运动的,之后物体向正方向运动,你带进去时间就可算出距离.
(3)-48ft/sec
(4)v=8πr,带进r的值就算出来了