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A sprinter runs a 100 m dash in 12.0 s. She starts from rest with a constant acceleration ax for 2.0 s and then runs with constant speed for the remainder of the race.

Answer :

Eduard22sly

the value of ax, given the data from the question is 4.55 m/s²

Data obtained from the queston

From the question given above, the following data were obtained:

  • Total distance travelled = 100 m
  • Total time = 12 s
  • Time for acceleration (t) = 2
  • Acceleration (a) = ax =?

How to determine the distance travelled in the first 2 s

  • Initial velocity = 0 m/s
  • Acceleration (a) = ax
  • Time (t) = 2 s
  • Distance (s) for the first 2 s = ?

s = ½at²

s = ½ × ax × 2²

s = 2ax

How to determine the velocity in the first 2 s

  • Acceleration (a) = ax
  • Time for acceleration (t) = 2 s
  • Velocity for the first 2 s (v) = ?

v = at

v = ax × 2

v = 2ax

How to determine the value of ax

Remaining distance = velocity × remaining time

Remaining time = 12 - 2 = 10

Remaining distance = 2ax × 10

Remaining distance = 20ax

Total distance = Distance for first 2 s + Remainng distance

100 = 2ax + 20ax

100 = 22ax

Divide both sides by 22

ax = 100 / 22

ax = 4.55 m/s²

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