The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m,

Question

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver's reaction time of 0.43 s .

Part A

What is the minimum stopping distance for the same car traveling at a speed of 38 m/s ?

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver's reaction time of 0.43 s .

Part A

What is the minimum stopping distance for the same car traveling at a speed of 38 m/s ?

Explanation / Answer

Let deceleration a.

Car travelled for 0.43s at 30 m/s. Distance covered = 30*0.43 = 12.9m

Distance in which it is brought to rest = 60-12.9 = 47.1m

Using the formula
v^2 - u^2 = 2*a*s (s = distance travelled = 47.1, v = 0, u )

a = -30^2/(2*47.1) = -9.554 m/s/s

Now, for the car travelling at 38 m/s, the reaction time is still 0.43s. Distance travelled due to that = 38*0.43 = 16.34m

Distance travelled friction be s. again using
v^2 - u^2 = 2*a*s (s = distance travelled, v = 0, u , a = -9.554)

s = -38^2/(2*-9.554) = 75.57m

Therefore, min stopping distance = 75.57+16.34 = 91.91m

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