Kinematics question about a runner

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In summary, a sprinter can accelerate with constant acceleration for 3.00 s before reaching top speed and can run the 100-meter dash in 10 s. To determine his speed as he crosses the finish line, the problem can be broken up into two parts: the constant acceleration part and the constant velocity part. By setting the total distance to be the sum of the distance traveled under each part, the acceleration can be determined using the average velocity formula. This can then be substituted into the formula that relates the squares of the velocities, distance, and acceleration. Rearranging for vf will give the final answer.
  • #1
MMVS
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Homework Statement


A sprinter can accelerate with constant acceleration for 3.00 s before reaching top speed. He can run the 100-meter dash in 10 s.

What is his speed as he crosses the finish line?

Homework Equations


U1L6a1.gif


The Attempt at a Solution


So I broken up the question into two parts, one where he has constant acceleration, the other where he has constant velocity.

idk where to go from there, can someone point me in the right direction?
 
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  • #2
You're approach to breaking the problem up into two parts is a good approach. You know that the first part of the spring takes three seconds, while the second portion at the top speed takes seven seconds. One approach would be to set the total distance to be the sum of the distance traveled under the constant acceleration part, and the distance traveled under the constant velocity part. This leaves you with determining the acceleration. This can be done by using the average velocity formula, (since the r.h.s. involves the quantities you either know or want), and substitute that into the formula that relates the squares of the velocities, distance, and acceleration. Sub in the distance, solve for a, and then plug into your distance formula. Then rearrange for vf and that should do it.
 
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  • #3
Technically in both parts the acceleration is constant.

Can you try and apply one of those kinematic equations you listed above?
 
  • #4
Thank you both for taking the time to reply! Your instructions led me in the right direction. I took the liberty of scanning my work so anyone else having trouble with this type of question can see the steps.
scan__1443369936_68.147.204.233.jpg
 
  • #5
scan__1443370275_68.147.204.233.jpg
 

Related to Kinematics question about a runner

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

2. How is kinematics related to a runner?

Kinematics can be applied to a runner's motion by analyzing their speed, velocity, acceleration, and displacement over a period of time.

3. What is the difference between speed and velocity?

Speed is the rate at which an object moves, while velocity is the speed in a specific direction. So, while a runner may have a constant speed, their velocity changes if they change direction.

4. How is acceleration calculated for a runner?

Acceleration is the rate of change of velocity over time and can be calculated by dividing the change in velocity by the change in time. For a runner, this could be their change in speed over a specific time interval.

5. How does displacement differ from distance?

Displacement is the change in an object's position from its starting point, while distance is the total length of the path traveled. So, while a runner may run a certain distance during a race, their displacement may be less if they end at the same point they started.

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