Q.29 A vehicle was stopped by fully jamming the breaks in 1.8 s and the skid marks measured 9 m. Determine the average skid resistance. Take g = 10 m/s².
- A0.278
- B0.556Correct
- C0.15
- D2.78
Solution
Concept
With uniform braking deceleration, skid friction f = a/g, where a comes from stopping time and skid length.
Formula
s = (v × t)/2 ; a = v/t = 2s/t2 ; f = a/g = 2s/(g t2)
Step-by-step solution
1. Vehicle stops fully, so final speed = 0. Take deceleration as uniform. 2. Distance s = (v × t)/2, so v = 2s/t = 2 × 9 / 1.8 = 10 m/s. 3. Deceleration a = v/t = 10 / 1.8 = 5.556 m/s². 4. Friction force gives deceleration: f × m × g = m × a, so f = a/g. 5. f = 5.556 / 10 = 0.556.
Explanation
The car slows down at a uniform rate until it stops. From time and skid length we get the initial speed and the deceleration. Skid resistance is deceleration divided by g, which is 0.556.
Why the other options are wrong
A (0.278): the factor 2 is missed (s = a t2 used instead of s = a t2/2). C (0.15): wrong formula or wrong arithmetic. D (2.78): friction coefficient this large is not realistic, and the value is wrong.
Shortcut
f = 2s/(g t2) = 2 × 9/(10 × 1.82) = 18/32.4 = 0.556
Common mistake
Forgetting the factor 2 in s = v t/2 gives 0.278.
Correct answer: B) 0.556