How fast will your twin crash into the overturned truck?

[freshcoast]

Homework Statement

You and your identical twin are driving identical cars with identical tires down a straight road on a foggy day. You are the more prudent of the two and are driving at a speed of 50 km/hr. Your twin decides to pass you and accelerates to a speed of 70 km/hr, which he maintains as he tries to pass. As his car draws level to yours, each of you sees an overturned truck blocking the road. You each apply the brakes at the same instant and begin to skid towards the truck. You manage to halt a few inches from the truck. Approximately how fast is your twin going when he crashes into it?

Homework Equations

Vf = Vo + at
Δx = Vot + 1/2at^2
Vf^2 = Vo^2 + 2aΔx

The Attempt at a Solution

for car 1 Vo = 50km/hr
for car 2 Vo = 70km/hr

So far all I can do is convert the velocities to meters per second, understand that for car 1 the final velocity would be 0. Both cars begin to brake at the exact same X initial which is not provided nor is a time or an acceleration rate. I don't if this problem is unsolvable due to not enough information but I can't seem to get any way to begin solving this problem, thanks in advance for any input

 

[gneill]

Homework Statement

You and your identical twin are driving identical cars with identical tires down a straight road on a foggy day. You are the more prudent of the two and are driving at a speed of 50 km/hr. Your twin decides to pass you and accelerates to a speed of 70 km/hr, which he maintains as he tries to pass. As his car draws level to yours, each of you sees an overturned truck blocking the road. You each apply the brakes at the same instant and begin to skid towards the truck. You manage to halt a few inches from the truck. Approximately how fast is your twin going when he crashes into it?

Homework Equations

Vf = Vo + at
Δx = Vot + 1/2at^2
Vf^2 = Vo^2 + 2aΔx

The Attempt at a Solution

for car 1 Vo = 50km/hr
for car 2 Vo = 70km/hr

So far all I can do is convert the velocities to meters per second, understand that for car 1 the final velocity would be 0. Both cars begin to brake at the exact same X initial which is not provided nor is a time or an acceleration rate. I don't if this problem is unsolvable due to not enough information but I can't seem to get any way to begin solving this problem, thanks in advance for any input

How might you find an expression for the acceleration (or deceleration) of the first twin?

 

[freshcoast]

I can use one of the constant acceleration equations but I am either missing the change of x or time.

 

[gneill]

I can use one of the constant acceleration equations but I am either missing the change of x or time.

Take a close look at your third Relevant Equation.

 

[freshcoast]

Got it! I solve for acceleration for car 1 using relevant eq. 3 and substitute it into the same equation but for car 2 and the change of x cancels out. Thanks!