Two cars driving toward each other (non-uniform speed)

[Stormblessed]

Homework Statement

Two cars are 1.4 km apart and driving towards each other. One car starts from rest and accelerates uniformly at 1.2 m/s^2. The other car is driving at a constant speed of 18 m/s. When will the cars meet?

Homework Equations

d=vt
d=ut + 1/2at^2
d=vt-1/2at^2
v^2 = u^2 + 2ad

Note: u is initial velocity and v is final velocity

The Attempt at a Solution

The answer provided by the teacher is 36 seconds. I don't know how to get there. I understand what to do if both cars have constant speed (create two equations equal to each other and solve for time) but I don't know what to do if one car is accelerating. If I use the algebraic method, I am getting 30 s instead of 36 s.

d1 = 1/2at^2
d1 = 1/2(1.2)t^2
d1 = 0.6t^2

d2 = vt
d2 = 18t

d1 = d2
0.6t^2 = 18 t
t = 30 s (which is incorrect)

 

[TSny]

d1 = d2

Why does each car have to travel the same distance?

Think about what d1 + d2 should equal.

 

[Stormblessed]

Why does each car have to travel the same distance?

Think about what d1 + d2 should equal.

Oh, so can the equation be written as:

0.6t^2 + 18 t = 1400

And then I just solve for t?

 

[TSny]

Give it a try.

 

[Stormblessed]

Give it a try.

Ok, this works (t = 35.5). Thanks a lot. So does this apply (d1 + d2 = dtotal) for all "two cars driving toward each other" questions?

 

[TSny]

Yes. So, when both cars travel with constant velocity, you would still set up d1 + d2 = initial separation distance.

However, there is another way to think about it. Introduce an x-axis and let the position of the cars on the axis be x₁ and x₂. Set up equations for x₁ and x₂ as functions of time. Then you would be looking for the time when x₁ = x₂.

The difference in these two approaches is that x represents position on the x-axis, whereas d represents distance traveled.