math word problem

Question

A car’s distance in relation to time is modeled by the following function: y = 5x^2 + 20x + 200, where y is distance in km and x is time in hours.

a) A police office uses her radar gun on the traveling car 4 hours into the trip. How fast is the car traveling at the 4 hour mark?

b) How fast was the car traveling 7 hours into the trip?

Answer 1

y(t)=5t^2 +20t +200

take the derivative of y, for speed or velocity

speed is y'(t) =10t +20

at 4 hours speed = y'(4)= 10(4)+20 = 60 km/hour

after 7 hours speed =y'(7) = 10(7) +20 = 90 km/hour