Efficiently Solve Your Car Lane Change Time Problem - 65.0 km/h vs 45.0 km/h

[motionman04]

How long does it take an automobile traveling in the left lane at 65.0 km/h to pull alongside a car traveling in the same direction in the right lane at 45.0 km/h if the cars' front bumpers are initially 100 m apart?

 

[faust9]

What have you done thus far?

 

[Pyrrhus]

Use Kinematic equations.

Both have constant speed so

$$v_{1}t = x$$ for the car on the right lane

$$v_{2}t = x + 100$$ for the car on the left lane

 

[motionman04]

Well I did some conversions to obtain 18.05 m/s as the velocity of the first car, but still kinda unsure of where to go from there.

 

[faust9]

Don't bother with conversions. You know the velocities. X for both cars is the same (that's why the second equation has the extra 100). The times will be the same. You are in a position with two equations and two unknowns. There are a handful of ways to solve this. You could use substitution, plug the coefficients into a matrix and rref it, solve simultaneously... Put all of the things you don't know on the left side with the respective coefficients. Leave the suff you do know on the right (like the 100). And solve.

Good luck.

 

[Spectre5]

but if you do not change the velocities to m/s then you must change the 100m to .1 km.

You could use relative motion...

the velocity of the left one with respect to the right is the velocity of the left minus the velocity of the right one...so 20km/hr. Then you want the relative velocity to go 100m (or .1 km)...so .1 km / 20 km/h should yield the correct answer in hours...convert to seconds by multiplying by 3600.