what distance should you keep between you and the car in front of you if the traffic is moving at 65mph? Your reaction time is 1s, and both the cars can decelerate at the same rate. Include reasonable estimate for the length of the car (you don't want your bumper to end up at the same location as the bumper or even the rear of the car in front of you).

65mph=29.05m/s
t=1s
a=constant
d=?

I am having trouble solving this problem. Would I use:
delta d = v_f^2 - v_0^2/(2a) But i don't think this is correct because there's no t and I also don't have a definite number for a. OR is the correct equation: d=d_0+v_0t+1/2at^2
but again I don't know a. Thanks in advance for your help. I really appreciate it.

To determine the appropriate distance to keep between you and the car in front of you, we need to consider the distance traveled during your reaction time and the distance required to bring your car to a complete stop.

Let's break down the problem step by step:

1. Reaction Time: Given that your reaction time is 1 second, during this time, your car will continue to move at its current velocity. In this case, the traffic is moving at 65 mph, which is equivalent to 29.05 m/s.

2. Distance Traveled during Reaction Time: To calculate the distance traveled during your reaction time, we can use the formula:

Distance = Velocity x Time

Distance = 29.05 m/s x 1s = 29.05 meters

3. Braking Distance: Next, we need to consider the distance required to bring your car to a complete stop. To calculate this distance, we can use the formula:

Distance = (Velocity^2) / (2 x Acceleration)

Since the car in front of you can decelerate at the same rate as your car, we need the deceleration of one car.

4. Estimating Deceleration: We don't have a specific value for the acceleration, but we can make a reasonable assumption. A typical passenger car can decelerate at around 4-5 m/s^2. For our calculation, let's assume a deceleration of 4 m/s^2.

5. Calculate Braking Distance: Using the deceleration value, we can calculate the braking distance:

Distance = (29.05^2) / (2 x 4) = 123.08 meters

6. Total Safe Distance: To determine the total safe distance, we need to add the distance traveled during your reaction time (29.05 meters) to the braking distance (123.08 meters):

Total Safe Distance = 29.05 meters + 123.08 meters = 152.13 meters

Therefore, you should maintain a distance of approximately 152.13 meters between your car and the car in front of you to ensure a safe space for both your reaction time and the braking distance.