- #1
Adjoint
- 120
- 3
Homework Statement
Two cars, A and B are traveling in same direction with velocities vA and vB. When car A is distance d behind car B, the breaks on A are applied, causing a deceleration a. Show that to prevent a collision between A and B, it is necessary that, vA - vB < [itex]\sqrt{2ad}[/itex]
Homework Equations
1D kinematics
The Attempt at a Solution
Suppose at the moment car A starts acceleration, it is at the origin, then car B is at x = d.
After time t, car A has position vAt - [itex]\frac{1}{2}[/itex]at2
Then car B has the position vBt + d
Now, to avoid collision, vBt + d > vAt - [itex]\frac{1}{2}[/itex]at2
→ vA - vB < [itex]\frac{1}{2}[/itex]at + [itex]\frac{d}{t}[/itex]
Now I have to remove t from this equation.
Any help please?
Thanks in advance.