Question

You are driving down the road at 30 mph (miles per hour) when you see the traffic light change to red. The red light is 300 feet from you. How much time will it take you to stop? (please provide explanation)

Answer 1

45 s

Step-by-step explanation:

To find the time it takes to stop, we first find the deceleration, a of the car from

v² = u² + 2as and a = (v² - u²)/2s were v = final velocity of car = 0 mph = 0 m/s, u = initial velocity of car = 30 mph = 30 × 1609.34 ft ÷ 3600 s = 13.41 ft/s and s = distance = 300 ft. Substituting the values into a, we ave

a = (v² - u²)/2s = (0² - 13.41²)/2×300 = -0.3 ft/s²

We then find the time for this deceleration from v = u + at ⇒ t = (v - u)/a

t = (v - u)/a = (0 - 13.41 ft/s)/-0.3 ft/s² = - 13.41 ft/s/-0.3 ft/s² = 44.7 s ≅ 45 s

So it takes 45 seconds to stop.