Suppose a car is traveling at +22.3 m/s, and the driver sees a traffic light turn red. After 0.351 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 8.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?
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To find the stopping distance of the car, we need to consider the initial velocity, the deceleration, and the time elapsed. The formula we can use is:
Stopping Distance = Initial Velocity × Time + (1/2) × Deceleration × Time²
Let's plug in the given values:
Initial Velocity (u) = +22.3 m/s (since it is given as positive, we assume it to be in the direction of motion)
Time (t) = 0.351 s
Deceleration (a) = -8.00 m/s² (negative because the car is decelerating, opposite to its initial motion)
Now substitute these values into the formula:
Stopping Distance = (22.3 m/s) × (0.351 s) + (1/2) × (-8.00 m/s²) × (0.351 s)²
Let's calculate this:
Stopping Distance = 7.82 m + (-0.984 m)
Stopping Distance = 6.836 m
Therefore, the stopping distance of the car, as measured from the point where the driver first notices the red light, is approximately 6.836 meters.