Velocity and Acceleration in a 100 Meter Dash

In summary: So it's a bit more complicated than that, but that's the gist of it.So, if I use 5m/s^2 and solve for velocity, I get 10m/s, then when I solve for the time, I get 10s. Is that right, because I got really confused when it mentioned constant acceleration and velocity.
  • #1
Tabe
42
0
Ok, I have this problem...
The first 10 meters of a 100 meter dash are covered in 2 seconds by a sprinter who starts from rest and acceleraties with a constant acceleration. The remaining 90 meters are run with the same velocity the stprinter had after 2 seconds.
a) Determin the sprinter's constant acceleration during the first 2 seconds.
b) Determine the sprinter's velocity after 2 seconds have elapsed.
c) Determine the total time needed to run the full 100 meters.

What I don't understand is the 'accelerates with a constant acceleration' part. All I did to solve that part was solve for the average acceleration, which I think is wrong.
I ended up getting 2.5 m/s^2 for the acceleration.

Could anyone tell me whether or not I'm on the right track, or if I'm totally wrong, just point me in the right direction.
 
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  • #2
Average acceleration? How did you get that? Anyway, you know the acceleration of the sprinter is constant, and you know the equation of position wrt time for an object at constant acceleration:

[tex]x(t) = x_0 + v_0t + 0.5at^2[/tex]

Use that and the data you know to retrieve a.


P.S. You should have posted this in the Homework section: https://www.physicsforums.com/forumdisplay.php?f=15

Even if it's not officially an homework, it's clearly a question taken from a textbook.
 
Last edited:
  • #3
Ok, I used that formula, and ended up getting 5 m/s^2. Is that what I should have gotten or did I mess up again somewhere.
 
  • #4
I get that too.
 
  • #5
So, if I use 5m/s^2 and solve for velocity, I get 10m/s, then when I solve for the time, I get 10s. Is that right, because I got really confused when it mentioned constant acceleration and velocity.
 
  • #6
Tabe said:
So, if I use 5m/s^2 and solve for velocity, I get 10m/s, then when I solve for the time, I get 10s. Is that right, because I got really confused when it mentioned constant acceleration and velocity.

Yes for speed, nope for time. Traveling 90 meters at speed 10m/s takes 9 seconds. And before that, he was accelerating for 2 seconds. So total time to complete the race: 9 + 2 = 11s.

What confuses you about the notions of constant acceleration and constant velocity? Perhaps we can sort that out.
 
  • #7
I accel. Get it? excel = accel. Ha ha I'm so lame.
 
  • #8
I really mix up and/or combine velocity and acceleration. The change from constant acceleration to constant velocity really confused me, because I know that acceleration can remain constant.
 
  • #9
I hear ya. Acceleration is the building of velocity, as told by the units of acceleration: x m/s² = x (m/s)/s. I.e. the object's speed gains x m/s every second. So if the acceleration is constant, the velocity is building at a constant rate. That is how the two are related. On the other hand, if the velocity is constant, it necessarily means that the acceleration is 0 (no building of velocity).
 

What is the difference between velocity and acceleration?

Velocity is a measure of an object's speed and direction, while acceleration is a measure of how much an object's velocity changes over time. In simpler terms, velocity tells us how fast an object is moving and in what direction, while acceleration tells us how much an object's speed or direction is changing.

How are velocity and acceleration related?

Velocity and acceleration are closely related because acceleration is the rate of change of an object's velocity. In other words, acceleration is the amount by which an object's velocity changes in a given amount of time. This means that if an object has a constant acceleration, its velocity will change by the same amount every second.

What are some real-world examples of velocity and acceleration?

Velocity and acceleration can be observed in many everyday activities. For example, when a car speeds up or slows down, it is experiencing acceleration. Similarly, when a ball is thrown into the air, it experiences both velocity (as it moves through the air) and acceleration (due to the force of gravity). These concepts are also important in sports, such as when a runner sprints or a skateboarder performs a trick.

How are velocity and acceleration calculated?

Velocity is calculated by dividing the distance an object has traveled by the time it took to travel that distance. Acceleration, on the other hand, is calculated by dividing the change in velocity by the time it took for that change to occur. This can be represented by the equation a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is the difference between average velocity and instantaneous velocity?

Average velocity is the average rate at which an object's position changes over a given period of time. It is calculated by dividing the total change in position by the total time elapsed. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time. It is calculated by taking the limit of the average velocity as the time interval approaches zero. In other words, instantaneous velocity is the average velocity at a specific point in time.

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