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,
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To find the time it takes for the car to reach the second traffic light, we need to determine the value of t when the car comes to a stop.
The equation that represents the speed of the car is s = -10/t - 8 + 80.
Since the car accelerates and then decelerates at a constant rate, we can assume that the car comes to a stop when its speed is zero. Therefore, we can set s = 0 and solve for t.
0 = -10/t - 8 + 80
To simplify the equation, let's first get rid of the fraction by multiplying every term by t:
0 = -10 - 8t + 80t
Next, let's collect like terms by combining the t-terms:
0 = 80t - 8t - 10
0 = 72t - 10
Now, let's isolate the variable t by moving the constant term to the other side of the equation:
10 = 72t
Finally, solve for t by dividing both sides of the equation by 72:
t = 10/72
Therefore, it takes the car approximately 0.14 (rounded to two decimal places) seconds to reach the second traffic light.