Collision in a One Lane Tunnel: How to Calculate Distance and Time?

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In summary, the conversation discusses the scenario of Speedy Sue driving at 30.0m/s and encountering a slow-moving van 155m ahead. It is determined that a crash will occur when Sue applies her brakes and accelerates at -2.00 m/s^2, but the exact displacement of the crash is unknown. The conversation then delves into finding equations for Sue's and the truck's position as functions of time in order to determine the time and distance of the crash. Finally, the conversation concludes with the suggestion of using basic kinematic equations to solve for the displacement of the crash.
  • #1
saber1357
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Homework Statement


Speedy sue, driving at 30.0m/s enters a one lane tunnel. She then observes a slow-moving van 155m ahead traveling at 5.00m/s. Sue applied her breaks and accelerates at -2.00 m/s^2. Will there be a collision? If yes, at what distance and what time?


Homework Equations


initial v = 30 m/s
final v = 0
a = -2/s^2
displacement = [(final velocity - initial velocity) / 2*acceleration)]

The Attempt at a Solution


By using the above equation, I found out that a crash does occur when Sue stops. However, I do not understand how to find out at exactly what displacement this crash occurs.
 
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  • #2
The position of the truck at a time t is given by xtruck(t)=155m+t*(5m/sec). I've picked x=0 to be the tunnel entrance and t=0 to be the time when Sue enters the tunnel. Can you write an equation for Sue's position at time t? Then set them equal and solve for t.
 
  • #3
Start by expressing Sue's displacement as a function of time and the truck's displacement as a function of time. At some time they end up in the same spot at the same time. (Measure the displacement of both from Sue's initial position.)
 
  • #4
I'm sorry, I don't understand. How can I express sue's, or the truck's displacement as a function of time?
 
  • #5
saber1357 said:
How can I express sue's, or the truck's displacement as a function of time?
Dick gave you the truck's position as a function of time. Now you find Sue's position as a function of time.
 
  • #6
I don't understand how Dick came up with that function :)
I want to say that the function for Sue's car is car(t) = t*30m/s, but that doesn't work out because I don't know how to incorporate the acceleration. Could you please explain how a function of time is created?
 
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  • #7
You must have some kinematical equations to use. The one I'm thinking of looks like:

x(t)=x0+v0*t+(1/2)*a*t^2.

Does that look familiar?
 
  • #8
You need to be familiar with the basic kinematic equations for constant speed and accelerated motion. Here's a summary that might prove helpful: Basic Equations of 1-D Kinematics
 
  • #9
aha! so the equation for the car will be car(t) = 30t + .5(-2 m/s^2)(t^2)?
 
  • #10
Exactly!
 
  • #11
Absolutely right.
 
  • #12
i love you all
 

FAQ: Collision in a One Lane Tunnel: How to Calculate Distance and Time?

1. Will there be a collision between Earth and another celestial body?

It is highly unlikely that there will be a collision between Earth and another celestial body in the near future. The chances of such an event are extremely low, and astronomers and scientists are continually monitoring the skies for any potential threats.

2. What would happen if there was a collision between two celestial bodies?

The effects of a collision between two celestial bodies would depend on the size and speed of the objects involved. In most cases, it would result in significant damage to both objects, potentially altering their orbits and causing widespread destruction on a planetary scale.

3. Are there any known potential collision events in the future?

There are currently no known potential collision events in the future that pose a significant threat to Earth. While there may be some near-Earth objects that come close to our planet, the chances of a collision are very low and would likely not cause any major damage.

4. How do scientists predict potential collisions between celestial bodies?

Scientists use a variety of methods to predict potential collisions between celestial bodies. These include analyzing trajectories and orbits of objects, using telescopes and other instruments to track their movements, and utilizing computer simulations to model potential impact scenarios.

5. What precautions are being taken to prevent collisions with potentially hazardous objects?

Astronomers and space agencies around the world are constantly monitoring the skies for potentially hazardous objects and tracking their movements. In addition, there are plans in place to potentially deflect or destroy any objects that pose a significant threat to Earth in the future.

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