A car is driving at a speed of 48.0 km/h toward an intersection just as the ligh

Question

A car is driving at a speed of 48.0 km/h toward an intersection just as the light changes from green to yellow. The driver has a reaction time of 0.750 s and the magnitude of the braking acceleration of the car is 5.50 m/s^2. Find the minimum distance x_min the car travels before coming to a stop after the light changes

please follow the rubric and draw a picture

Setup 11/11 Solve 5/5 Reflect 4/4 Picture 2/2 Labeled quantities with variables defined 2/2 Setting up correct formulas 6/6 Headings 1/1 Showed unit check 2/2 Justified your answer (why does it make sense; compare with something familiar) 2/2 Reporting correct units 2/2 · .Getting math correct 3/3 .

Explanation / Answer

First, convert the speed to m/s: (48 km/h)(1000 m / 1 km)(1 h / 3600 s) = 13.3 m/s.
During the 0.750 s of reaction time, the car moves (13.3 m/s)(0.75 s) = 17.7 m.
Now use the formula for speed as a function of acceleration and distance: v² = 2ax. (This works for acceleration and deceleration problems both. Here, the speed is what would be achieved in a distance x with positive acceleration.)
v = 13.3 m/s; a = 5.50 m/s² (presented as if positive instead of negative, but it still works), so
v² = 2ax, or x = v²/(2a)
= (13.3 m/s)² / (2(5.50 m/s²))
= 16.1 m.

Add this to the reaction-time distance to get the total: 17.7 m + 16.1 m = 33.78 m. Round this to 34 m because only 2 significant figures are justified.

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