The function #D(t) = 13t^2-140t# gives the distance a car going a certain speed will skid in #t# seconds. How long would it take for the car to skid 180 feet?

1 Answer
Fleur
Jul 7, 2017

#~~11.9 s#

Explanation:

Substitute #180# for #D(t)#:

#180 = 13t^2 - 140t#
#0 = 13t^2-140t-180#

Use the quadratic formula to find the value of #t#:

#t=(-b+-sqrt(b^2-4ac))/(2a)#

#=(140+-sqrt((-140)^2-4(13)(-180)))/(2(13))#

#=(140+-sqrt(28960))/(26)#

#~~11.9 s # or #-1.2 s#

Eliminate #-1.2# seconds, since time cannot be negative. The car would skid #180# ft in about #11.9# seconds.

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