I'm kinda confused on how to set up this problem...

Question

If you had a collision that set off your airbag, you acceleration would be at least - 7g. How far would your car travel during a -7g collision? Acceleration of gravity is 9.8 m/s^2. How far would your car travel during a -7g collision at 20 m/s?

Since the car was in a collision, then the car had to come to a come to  complet stop right, so v2^2 = 0.

0 = v1^2 + 2a * change in displacement. ( i need to get the change in displacement on the other side of the equation.

change in displace = - v1^2 / 2a.... right?

Answer 1

We can evaluate the distance travelled by car using equation of motion ⇒ v² - u² = 2as .

The final velocity of the car after collision is (v) 0 .

So 0² - u² = 2as ⇒ s = -u² / 2a ⇒ s = -u² / 2(-7g) 

 s = u² / 14g 

The initial velocity of car is 20 m/s .

Acceleration due to gravity is 9.8 m/s² .

s = (20)² / 14(9.8)

s = 400 / 137.2 

s = 2.91 m .

Hence the distance travel by car after collision is 2.91 m .