Can You Calculate the Maximum Time Before a Car Hits an Accelerating Dragster?

[mrjoe2]

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

You drive at a constant speed of v0 toward the stopped dragster, not slowing down in the face of the imminent collision. The dragster driver sees you coming but waits until the last instant to put down the hammer, accelerating from the starting line at constant acceleration, a . Let the time at which the dragster starts to accelerate be t=0 .

What is tmax, 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?

 

[anathema]

I must advise against attempting this experiment as it could result in serious injury or even death. However, I can provide some calculations to demonstrate the potential acceleration of a top fuel drag racer.

First, let's assume that the initial velocity of the scientist's car is v0 = 50 m/s (112 mph). We will also assume that the dragster's acceleration is a = 50 m/s^2 (5.1 g), which is a typical acceleration for a top fuel drag racer.

Using the equation v = u + at (where v is final velocity, u is initial velocity, a is acceleration, and t is time), we can calculate the time it takes for the dragster to reach a speed of v = 50 m/s from a standing start:

50 = 0 + 50t
t = 1 second

This means that the dragster will reach a speed of 50 m/s in just 1 second, which is an incredibly short amount of time.

Now, let's consider the maximum time (tmax) that the scientist's car can continue at its initial velocity before colliding with the dragster. To calculate this, we can use the equation s = ut + 1/2at^2 (where s is distance, u is initial velocity, a is acceleration, and t is time).

Since the dragster is not moving initially, the distance it covers in time t will be equal to the distance between the scientist's car and the dragster when the dragster starts to accelerate. Let's assume this distance is d = 10 meters.

Plugging in the values, we get:

10 = 50t + 1/2(50)t^2
t^2 + t - 1 = 0

Using the quadratic formula, we get two possible solutions for t:

t = 0.618 seconds or t = -1.618 seconds

Since time cannot be negative, we can ignore the second solution and conclude that the longest time (tmax) the scientist's car can continue at its initial velocity before colliding with the dragster is approximately 0.618 seconds.

In conclusion, this experiment would demonstrate the tremendous acceleration of a top fuel drag racer, but it is not worth the risk of injury or death. It is important to always prioritize safety when conducting experiments.

 

[baba89]

I would approach this question by first identifying the key variables and equations involved. The key variables in this scenario are the initial velocity of the scientist's car (v0), the constant acceleration of the dragster (a), the time at which the dragster begins to accelerate (t=0), and the maximum time (tmax) at which the scientist's car can collide with the dragster if it continues at its initial velocity. The relevant equation for this scenario is the equation for distance traveled with constant acceleration: d = v0t + 1/2at^2.

Using this equation, we can calculate the distance that the dragster travels from the starting line in the time tmax: d = 1/2atmax^2. We can also calculate the distance that the scientist's car travels in the same time tmax: d = v0tmax. Since the goal is for the scientist's car to collide with the dragster, these two distances must be equal: 1/2atmax^2 = v0tmax.

Solving for tmax, we get tmax = 2v0/a. This means that the longest time after the dragster begins to accelerate that the scientist's car can collide with the dragster is 2v0/a. In other words, if the scientist's car continues at its initial velocity, it will take 2v0/a seconds for it to reach the same distance as the dragster from the starting line.

In conclusion, the maximum time (tmax) at which the scientist's car can collide with the dragster is 2v0/a seconds. This demonstrates the tremendous acceleration of the dragster, as it can cover a significant distance in a short amount of time compared to the scientist's car.