A drag racer accelerates at​a(t)equals=7272​ft/ssquared2.Assume that​v(0)equals=0and​s(0)equals=0. a. Determine the position function fortgreater than or equals≥0.b. How far does the racer travel in the first66​s?c. At this​ rate, how long will it take the racer to travelone third13​mi?d. How long will it take the racer to travel300300​ft?e. How far has the racer traveled when it reaches a speed of183183​ft/s?

Question
Asked Nov 25, 2019
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A drag racer accelerates at
​a(t)equals=7272
​ft/ssquared2.
Assume that
​v(0)equals=0
and
​s(0)equals=0.
 
a. Determine the position function for
tgreater than or equals≥0.
b. How far does the racer travel in the first
66
​s?
c. At this​ rate, how long will it take the racer to travel
one third13
​mi?
d. How long will it take the racer to travel
300300
​ft?
e. How far has the racer traveled when it reaches a speed of
183183
​ft/s?
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Expert Answer

Step 1

(a)

Given information:

A drag racer accelerates at a(t)...

Calculate:
First, we have to find the speed of racer by integrating the acceleration with respect
to t
v(t)=Ja(t)d
-72dt
72t
Now, find the position by integrating the speed with respect to t
t
s()=v(t)dt
0
72tdt
0
= 36t
Therefore, the position of race is s(t) =36t2
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Calculate: First, we have to find the speed of racer by integrating the acceleration with respect to t v(t)=Ja(t)d -72dt 72t Now, find the position by integrating the speed with respect to t t s()=v(t)dt 0 72tdt 0 = 36t Therefore, the position of race is s(t) =36t2

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