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The Equations of Motion

On a foggy da...

Question

On a foggy day, two car drivers spot each other, when they are just 80 m apart. They are traveling at 72 km/h and 60 km/h respectively towards each other. Both of them simultaneously apply brakes, which retard both the cars at a rate of 5 m/s². Determine whether they avert the collision or not.

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Solution

Lets find the distance travelled by both before they come to a halting stop.

Car 1:

u = 72kmph = 20 m/s

a = -5m/s2

v2-u2=2as

02-202=2(-5)s

s = 40 m

Car 2:

u = 60kmph = 16.66 m/s
a = -5m/s2

v2-u2=2as

02-16.62=-25*s

s = 27.7 m

So total distance travelled = 40+27.7 = 67.5 m

Since they are 80 m apart and sum of both their distance is less than 80, they would stop before time.

There would no collision.
Thank you.

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