How far does he run during the acceleration phase?

In summary, the conversation is about a sprinter's race where they accelerate from rest to a top speed with an acceleration of 3.50 m/s2. The total race is 100 meters long and takes 17.00 seconds. The conversation includes setting up equations for the acceleration phase and the constant speed phase to determine how far the sprinter runs during the acceleration phase. The equations used are s(t) = 3.5/2 * t^2 for the acceleration phase and s(t) = [3.5*t(a)]*[t-t(a)] + 3.5/2*t(a)^2 for the constant speed phase. The sprinter's speed and distance are determined using these equations.
  • #1
dvbballgurl11
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If anyone could help it would be greatly appreciated! A sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 3.50 m/s2. After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is one hundred meters long. If the total race is run in 17.00 s, how far does he run during the acceleration phase?
 
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  • #2
well I'd start by setting up the equations of motion in two parts: the accelaration phase and the constant speed phase:
ie: for 0<t<t(a) s(t) = 3.5/2 * t^2 [t(a) is the time they stop accelarating]..
do the same for the constant speed (its a bit more complicated) and using your known values see what you can do
 
  • #3
hey i tried doing that but cannot seem to come up with the right answer. any ideas?
 
  • #4
well, when you are done accelerating what is your speed? (using t(a) as a variable) and how far have you gone? (again using t(a) and the 1st equation)
 
  • #5
i don't know i keep getting confused on what to plug in where. any chance on getting help setting up the equations?
 
  • #6
something like this
0<t<t(a) s(t)=3.5/2 t^2
t(a)<t<t(f) s(t) = [3.5*t(a)]*[t-t(a)] + 3.5/2*t(a)^2
 

FAQ: How far does he run during the acceleration phase?

1. How is the distance traveled during acceleration phase calculated?

The distance traveled during the acceleration phase is calculated using the formula d = 0.5 * a * t^2, where d is the distance, a is the acceleration, and t is the time.

2. What factors affect the distance traveled during acceleration phase?

The distance traveled during the acceleration phase can be affected by various factors such as the initial velocity, the acceleration rate, and the duration of the acceleration phase.

3. Can the distance traveled during acceleration phase be negative?

No, the distance traveled during the acceleration phase cannot be negative as it represents the magnitude of the displacement and is always a positive value.

4. How does the distance traveled during acceleration phase differ from the total distance traveled?

The distance traveled during the acceleration phase only considers the distance covered while accelerating, while the total distance traveled takes into account the distance covered during the entire motion, including the acceleration and deceleration phases.

5. Is the distance traveled during acceleration phase equal to the displacement?

Yes, if the acceleration phase is the only phase of motion, then the distance traveled during acceleration phase is equal to the displacement. However, if there are other phases of motion involved, the displacement may be different from the distance traveled during the acceleration phase.

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