Name: Lisa Who is asking: Student
Question: Hi Lisa,
Below is a diagram that shows the two cars, at time t = 0, just as the light changes, and at time t a short time later (your car is green, the other is red). The length of your car is c miles. At time t the red car is travelling v miles per hour, you are travelling at v_{1} miles per hour, the red car's acceleration is r miles per hour squared and your acceleration is r_{1} miles per hours squared . Also the red car has travelled s miles and you have travelled s_{1} miles.
Since you must be "one car length away from the car in front of you for every 10 miles per hour", the distance from you to the red car is ^{c v1}/_{10} miles. Hence, from the diagram
Differentiating both sides with respect to t gives
