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Quadratic Equation (Application in Physics)

Q23 WK6 in Level II session:

The braking distance d is given by: d = 0.044v² + 1.1v where v is speed in miles per hour.

For braking distance to be 165 feet, we can use the above equation to find the maximum speed v (in feet per sec and convert that to miles per hour).

Therefore 165 = 0.044v² + 1.1v.
    => 15 = 0.004v² + 0.1v
    => 15000 = 4v² + 100v
    => 4v² + 100v − 15000 = 0
    => v² + 25v − 3750 = 0 (Note −3750 = −10 × 15 × 25 or −50 × 75)

    => (v + 75)(v − 5) = 0
    => v = −75 or v = 50 (neglecting negative speed)
    => v = 50 feet/sec
    => v = 50 × 3600 / 5280 miles/hour or ~34 miles/hour

Quadratic Equation (Application in Physics)

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