Physics of a runner (Constant Acceleration/ constant velocity)

In summary, the problem involves a 100-meter dash where a 64-meter sprinter accelerates uniformly for the first 41 meters and maintains top speed for the remaining 59 meters. The problem does not provide enough information to solve for the average horizontal component of force or the speed of the sprinter over the last 59 meters. To solve for these, additional information, such as the time taken for the sprinter to reach top speed, is needed.
  • #1
Cllzzrd
7
0

Homework Statement


"The 100- dash can be run by the best sprinters in 10.0 . A 64- sprinter accelerates uniformly for the first 41 to reach top speed, which he maintains for the remaining 59 ."

What is the average horizontal component of force exerted on his feet by the ground during acceleration?

What is the speed of the sprinter over the last 59 of the race (i.e., his top speed)?


Homework Equations



F=ma
v=Vi+at
Xo=Xi+Vit+.5at^2
Vo^2=Vi^2+2a(Xo-Xi)

The Attempt at a Solution



I honestly have no idea how to even start this problem.

For the part where the runner is accelerating, here is what I have
Xi-0
Xo-41
Vi-0
Vo-?
a-?
t-?

Which is not much... For when he is at a constant speed, here is what I have.

Xi-41
Xo-100
Vi-?
Vo- ? (the same as Vi, as he is at a constant velocity)
a-0
t-?

So Xo=.5at
41=.5at

Vo=at
a=Vo/t

Vo^2=Vi^2+2a(Xo-Xi)
Vo^2=0+2(Vo/t)(41)

I am completely stuck... I have no idea where to go from here. Am I just looking at it wrong, or is there some important part that I missed?
 
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  • #2
just assume the topspeed is equal to v. Compute the total time taken as a function of v and set that equal to 10 seconds.
 

1. What is the difference between constant acceleration and constant velocity?

Constant acceleration refers to a situation where an object's velocity is changing at a constant rate. This means that the object's speed is increasing or decreasing by the same amount over equal intervals of time. On the other hand, constant velocity means that an object's speed and direction of motion remain the same over time. This means that the object is moving at a steady pace without any change in its speed or direction.

2. How does constant acceleration affect a runner's speed?

Constant acceleration can have a significant impact on a runner's speed. If a runner is experiencing constant acceleration, their speed will either increase or decrease at a constant rate. This means that their final speed will depend on the magnitude and direction of the acceleration. For example, if a runner is experiencing a constant acceleration of 2 meters per second squared, their speed will increase by 2 meters per second every second.

3. How does the force of gravity affect a runner's motion?

The force of gravity plays a crucial role in a runner's motion, especially when it comes to constant acceleration. Gravity is a force that pulls objects towards the center of the Earth. When a runner is running on a flat surface, the force of gravity is balanced by the normal force from the ground, allowing the runner to maintain a constant velocity. However, when a runner is running on an incline or decline, the force of gravity will cause the runner to experience a constant acceleration in the direction of the incline or decline.

4. Can a runner maintain a constant velocity for an extended period?

Yes, a runner can maintain a constant velocity for an extended period as long as the net force acting on them is zero. This means that the runner's speed and direction of motion will remain the same. However, any external forces such as air resistance or friction can cause the runner's velocity to change and make it difficult to maintain a constant velocity.

5. How does air resistance affect a runner's motion?

Air resistance, also known as drag, can significantly affect a runner's motion. When a runner is moving at high speeds, the air particles around them create a force that opposes their motion. This force can slow down the runner and make it difficult to maintain a constant velocity. To minimize the effects of air resistance, runners often use techniques such as running in a crouched position or wearing tight-fitting clothing to reduce drag.

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