Can You Calculate the Reaction Time Needed to Avoid a Deer at 18 m/s?

In summary, the question asks for the reaction time of a motorist who is traveling at 18 m/s^2 and sees a deer 38 m ahead, with a maximum negative acceleration of -4.5 m/s^2. The suggested equations are x(t)=x0+v0t+1/2at^2 and v=u+at, but the answer is actually 0.1111 s. There are multiple ways to solve this problem, but one approach is to calculate the distance traveled while decelerating at -4.5 m/s^2, and then subtract it from the total distance to find the remaining distance, which is equal to the reaction time.
  • #1
meggy8716
5
0
A motorist is traveling at 18 m/s^2 when he sees a deer 38 m ahead. If the maximum negative acceleration is -4.5 m/s^2, what is the reaction time (delta t) of the motorist that will allow him to avoid hitting the deer? Answer in units of 's'.

I tried using x(t)=x0+v0t+1/2at^2 and it didn't work out for me. I know the answer is supposed to be 0.1111 s and I can't get this no matter what I try. help!
 
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  • #2
trying using v = u +at and s = 0.5( u+v) t
and 0.1111s actually is 1/9 or 2/18 or ...
 
  • #3
Mjsd...that makes sense to me except I don't understand why 's' is equal to '1'?? Also, in the s = 0.5 (u+v)t equation I would think that acceleration should be used somewhere in the equation since that is how fast it is decelerating.
My original idea was the use the equation I mentioned above and then use the quadratic equation to get the answer, but that didn't work out so well.
 
  • #4
Please don't double, triple post the same question.
 
  • #5
firstly, let's remember that there are many ways to do the same problem. My way is to do it in two steps. By the way the equations I listed are correct, the second one is just: distance traveled = av. speed x total time.

Logic: how long does it take to stop from initial speed assuming the full [tex]-4.5m/s^2[/tex], then in that time how far the vehicle will travel, then what's left for reaction time? etc...
 

FAQ: Can You Calculate the Reaction Time Needed to Avoid a Deer at 18 m/s?

How do I solve a 1D kinematics problem?

Solving a 1D kinematics problem involves breaking down the problem into smaller parts and using the equations of motion to solve for the unknown variables. It is important to carefully read and understand the given information and identify what is known and what needs to be solved for. Then, choose the appropriate equation(s) and plug in the values to solve for the unknown variable.

What are the equations of motion used in 1D kinematics problems?

The four main equations used in 1D kinematics problems are:
- v = u + at (equation for final velocity)
- s = ut + 1/2at2 (equation for displacement)
- v2 = u2 + 2as (equation for final velocity squared)
- s = (u + v)t/2 (equation for average velocity)

What is the difference between average velocity and instantaneous velocity?

Average velocity is the total displacement divided by the total time taken, while instantaneous velocity is the velocity at a specific moment in time. Average velocity considers the entire motion, while instantaneous velocity only considers a specific point in the motion. Average velocity can also be calculated by finding the slope of the position-time graph, while instantaneous velocity can be found by finding the slope of the tangent line at a specific point on the graph.

When should I use the kinematic equations and when should I use graphs to solve a 1D kinematics problem?

The choice between using kinematic equations or graphs to solve a 1D kinematics problem depends on the given information and the type of problem. If the problem involves finding specific values such as initial velocity, final velocity, acceleration, or displacement, then kinematic equations are more appropriate. If the problem involves understanding the overall motion and the relationship between displacement, velocity, and acceleration, then graphs can be more useful.

How do I know if my answer is correct for a 1D kinematics problem?

To check if your answer is correct, you can use the given information and the equations of motion to solve for the same variable. If the results match, then your answer is most likely correct. You can also use common sense and logic to ensure that your answer makes sense in the context of the problem. Additionally, double-checking your calculations and units can help to confirm the accuracy of your answer.

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