Question

To demonstrate the tremendous acceleration of a top fuel dragracer, you attempt to run your car into the back of a dragster thatis "burning out" at the red light before the start of a race.(Burning out means spinning the tires at high speed to heat thetread and make the rubber sticky.)

You drive at a constant speed of v0 toward the stopped dragster, not slowingdown in the face of the imminent collision. The dragster driversees you coming but waits until the last instant to put down thehammer, accelerating from the starting line at constant
acceleration,a. Let the time at which thedragster starts to accelerate be t=0.
A) What is tmax, the longest time after thedragster begins to accelerate that you can possibly run into theback of the dragster if you continue at your initial velocity?
B) Assuming that the dragster has started at the last instantpossible (so your front bumper almost hits the rear of thedragster at t = tmax), find your distance from thedragster when he started. If you calculate positions on the way tothis solution,
choose coordinates so that the positionof the drag car is 0 at t = 0. Remember that you are solvingfor a distance (which is a magnitude, and can never be negative),not a position (which can be negative).

Answer 1

To determine the longest time after the dragster begins to accelerate that you can run into the back of the dragster if you continue at your initial velocity, consider the motion of both vehicles and calculate the distance between you and the dragster.

Step-by-step explanation:

In order to determine the longest time after the dragster begins to accelerate that you can possibly run into the back of the dragster if you continue at your initial velocity, we need to consider the motion of both vehicles.

Since you are driving at a constant speed towards the dragster, the distance between you and the dragster will remain constant until the dragster starts to accelerate. Once the dragster begins to accelerate, the distance between you and the dragster will start increasing at a certain rate.

The longest time you can possibly run into the back of the dragster is when the distance between you and the dragster becomes equal to the initial distance between you and the dragster at the moment the dragster starts to accelerate.