Answer:
The car come to a stop in 12.5 seconds after the driver applies the brakes
Step-by-step explanation:
Given :The position of the car is \(s(t) = 50t - 2t^ 2\), t seconds after the driver applies the brakes.
To Find : How many seconds after the driver applies the brakes does the car come to a stop?
Solution:
\(s(t) = 50t - 2t^ 2\)
\(V =\frac{ds}{dt}\)
Where V is Speed of car
So, \(V =\frac{d(50t - 2t^ 2)}{dt}\)
\(V =50-4t\)
So,Speed of the car is \(V =50-4t\)
Now we are supposed to find How many seconds after the driver applies the brakes does the car come to a stop.
So, Substitute V = 0
\(0 =50-4t\)
\(4t=50\)
\(t=\frac{50}{4}\)
\(t=12.5\)
Hence the car come to a stop in 12.5 seconds after the driver applies the brakes
