The equation you need to solve is:
d = 43t - 5t^2
To find the total distance traveled, you need to integrate this equation. The integral of d is:
D = 43t^2/2 - 5t^3/3
To find the total distance traveled before coming to a complete stop, you need to set t = 0 and t = the time it takes for the car to come to a complete stop. To find the time it takes for the car to come to a complete stop, you need to solve the equation:
43t - 5t^2 = 0
This equation can be solved using the quadratic formula:
t = (43 ± √(43^2 - 4(5)(0))/2(5)
t = (43 ± √1849)/10
t = 8.3 or t = 0
Since t = 0 is not a valid solution, the time it takes for the car to come to a complete stop is 8.3 seconds.
To find the total distance traveled before coming to a complete stop, plug t = 8.3 into the equation for D:
D = 43(8.3)^2/2 - 5(8.3)^3/3
D = 1745.7 feet
A car traveling at 43 ft/sec decelerates at a constant 5 feet per second squared. How many feet does the car travel before coming to a complete stop?
i tried a few different equations, none of the worked.
43t - 5t^2 = 0
43 - 10t = 0
21.5t^2 - (5/3)t^3 = 0
maybe im not supposed to set it to zero? i don't know what to do
This looks like the "anti-derivative" question I answered earlier this evening.
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