Question

What is relative velocity? Suppose you want to design an airbag system that can protect the driver in a head on collision at a speed of 100 km/hr or 60 mph. Estimate how fast the airbag must inflate to effectively protect the driver? The car crumples within a distance of 1m.

Answer 1

Answer:

0.072 seconds

Explanation:

t = Time taken

u = Initial velocity = 100 km/h

v = Final velocity

s = Displacement = 1 m

a = Acceleration

$v^2-u^2=2as\\\Rightarrow a=\dfrac{v^2-u^2}{2s}\\\Rightarrow a=\dfrac{0^2-(\dfrac{100}{3.6})^2}{2\times 1}\\\Rightarrow a=-385.802469136\ m/s^2$

$v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-\dfrac{100}{3.6}}{-385.802469136}\\\Rightarrow t=0.072\ s$

The time taken is 0.072 seconds