6. (6P) Formula Based Problem: A car is speeding down a highway at 30 m/s. A stray dog runs into the road ahead of the driver. The driver hits the brake decelerating at a rate of
10m/s. The driver managed to stop the car right as it was about to hit the car. How far
away was the dog when the driver first hit the brake?

45 m

Explanation:

From the question given above, the following data were obtained:

Initial velocity (u) = 30 m/s

Deceleration (a) = –10 m/s²

Final velocity (v) = 0 m/s

Distance (s) =?

The distance of the dog from the car before the driver hits the brake can be obtained as follow:

v² = u² + 2as

0² = 30² + (2 × –10 × s)

0 = 900 + (–20s)

0 = 900 – 20s

Collect like terms

0 – 900 = –20s

–900 = –20s

Divide both side by –20

s = –900 / –20

s = 45 m

Therefore, the dog was 50 m away when the driver first hit the brake

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