Car collision-speed passenger crashes into dashboard

[physicsquest]

Homework Statement

In a collision, an automobile initially traveling at 50 km/h decelerates at a constant rate of 200 m/s^2. A passenger not wearing a seat belt crashes against the dashboard. Before the collision, the distance between the passenger and the dashboard was 0.60 m. With what speed, relative to the automobile, does the passenger crash into the dashboard? Assume that the passenger has no deceleration before contact with the dashboard.

Homework Equations

x-x0= 1/2(v0+v)t
a= (v^2-v0)/2(x-x0)
50 km/h= 13.89 m/s

The Attempt at a Solution

-200m/s^2= (v^2-179.3 m^2/s^2)/1.2m

answer is supposed to be 15.5 m/s

 

[rl.bhat]

Final velocity of the passenger with respect to the automobile is zero. Find the initial velocity. It is not 50 km/h, because the automobile is retarding.

 

[physicsquest]

How do you calculate initial velocity without time given?

 

[rl.bhat]

How do you calculate initial velocity without time given?

Use second relevant equation.