What is the sprinter's speed at the finish line?

In summary, The problem involves finding the speed of a sprinter at the finish line, given that he can accelerate with constant acceleration for 3.8 seconds and can run the 100 meter dash in 15.0 seconds. To solve this, the problem can be divided into two intervals, with unknown variables being the acceleration for the first interval, the distance the sprinter begins running at top speed, and the speed at the finish line. By using the fact that d1+d2=100 and t1+t2=15s, a system of two equations can be created to solve for the unknown variables.
  • #1
pingpong240
27
0
Here is the problem I am trying to do:
A sprinter can accelerate with constant acceleration for 3.8 s before reaching top speed. He can run the 100 meter dash in 15.0 s. What is his speed as he crosses the finish line?

I'm currently trying to break this into two separate intervals. I believe the variables I am trying to find are the acceleration for the first interval, the distance that the sprinter beings running at top speed, and of course that speed. I'm trying kinematic equations but I always seem to end up with two unknowns in the same equation. A little push in the right direction is much appreciated! : )
 
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  • #2
Are you making use of the fact that d1+d2=100, and t1+t2=15s? It would be helpful if you showed more of your work.
 
  • #3
You are already headed in the right direction. You know there will be two functions of positions, one with acceleration, and one with a constant velocity. Together these will add up to the total distance. Two equations, and two unknowns (acc and vel).
 
  • #4
OK...sounds like I should consider a system of two equations and possibly combine them into one with variables that I know...
 
  • #5
Well yes, you must have at least two equations if you have two unknowns. As far as I know there aren't infinite solutions to the velocity vector. What did you come up with?
 
  • #6
No answer yet. I just expressed velocity over the first interval as 3.8a, now I am trying to represent the change in distance over that first interval in terms of a as well, and hopefully solve for a. Is this the right way so far?

EDIT: Didn't work for me.
 
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  • #7
Never mind I figured it out. Thanks for your help! ;)
 

FAQ: What is the sprinter's speed at the finish line?

What is the Sprinter Kinematics Problem?

The Sprinter Kinematics Problem is a physics problem that involves calculating the motion of a sprinter given their initial position, velocity, acceleration, and time. It is typically used to analyze the performance of sprinters in track and field events.

What are the key equations used in the Sprinter Kinematics Problem?

The key equations used in the Sprinter Kinematics Problem are the equations of motion, which include the displacement formula (x = x0 + v0t + 1/2at2), the velocity formula (v = v0 + at), and the acceleration formula (a = (v-v0)/t).

How do you solve the Sprinter Kinematics Problem?

To solve the Sprinter Kinematics Problem, you must first identify the known values (initial position, velocity, acceleration, and time) and the unknown value. Then, you can use the equations of motion to calculate the unknown value. It is important to pay attention to units and use appropriate units in your calculations.

What are some common misconceptions about the Sprinter Kinematics Problem?

One common misconception about the Sprinter Kinematics Problem is that it only applies to sprinters. In reality, the principles and equations used in this problem can be applied to any moving object. Another misconception is that acceleration is always constant, when in fact it can vary depending on the motion of the object.

How does air resistance affect the Sprinter Kinematics Problem?

Air resistance can affect the Sprinter Kinematics Problem by slowing down the sprinter and decreasing their acceleration. This can result in a slower overall time for the sprinter. However, in most cases, the effect of air resistance on a sprinter is minimal and can be ignored in calculations.

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