Question

Step 1

**Given information:**

Brain injuries occur when acceleration (a) reaches: **100g m/s ^{2}.**

Where g = **9.81 m/s ^{2}**

Distance travelled by the brain when the air bag is present (S_{1}): 20 cm = **20 × 10 ^{-2} m**

Distance travelled by the brain when there is no air bag (S_{2}): 5 cm = **5 × 10 ^{-2} m**

Maximum speed the car can have before hitting the barrier (u): ?

The final velocity (v) in both the cases: 0 m/s.

From equations of motion we know that

v^{2} – u^{2} = 2as

Step 2

Part A: Maximum speed the car can have before hitting the barrier, when the air bag is present:

Substituting the corresponding values in equation of motion mentioned:

v^{2} – u^{2} = 2aS_{1}

(0)^{2} – u^{2} = 2(-100g) (20 × 10^{-2} m)

NOTE: - “a” is negative because it is retardation.

We get:

u = 19.8 m/s

Step 3

Part B: Maximum speed the car can have before hitting the barrier, when the air bag is absent:

Substituting the corresponding values in equation of motion mentioned:

v2 &ndas...

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