when a traffic light turns green, a car accelerates at a constant rate, the decelerates in the same manner to stop at the next traffic light. The speed of the car, s, is given by the equation, s=-10 /t-8/ + 80 where t is time. Find the time , t, it takes for the car to reach the second light,
To find the time it takes for the car to reach the second traffic light, we need to determine when the speed "s" of the car becomes zero. In other words, we need to find the value of "t" that satisfies the equation:
s = -10/(t - 8) + 80
To solve the equation, we can start by setting the speed "s" to zero and solving for "t":
0 = -10/(t - 8) + 80
First, let's simplify the equation by multiplying through by (t - 8) to eliminate the denominator:
0 = -10 + 80(t - 8)
Distribute 80 to both terms:
0 = -10 + 80t - 640
Combine like terms:
0 = 80t - 650
Now, let's isolate the variable "t" by subtracting 80t from both sides:
80t = 650
Finally, divide both sides by 80:
t = 650 / 80
Simplifying the division:
t ≈ 8.125
Therefore, it takes approximately 8.125 seconds for the car to reach the second traffic light.