Question

What is the average acceleration of a sprinter that can reach a top speed of about 11.5 m/s in the first 19.0m of a race?

Answer 1

Approximately
`3.48\; {\rm m\cdot s^(-2)}`.

Step-by-step explanation:

Assume that the acceleration of this sprinter is constant during that part of the run. The following SUVAT equation would relate the acceleration
`a` of this person to initial velocity, final velocity, and the change in position:

`\displaystyle a = (v^(2) - u^(2))/(2\, x)`,

Where:

• 
  `v` is the final velocity,
• 
  `u` is the initial velocity, and
• 
  `x` is the change in position, also referred to as displacement.

For the sprinter in this question:

• 
  `v = 11.5\; {\rm m\cdot s^(-1)}` is the final velocity of the sprinter after traversing that first
  `19.0\; {\rm m}`,
• 
  `u = 0\; {\rm m\cdot s^(-1)}` assuming that this sprinter started from rest, and
• 
  `x = 19.0\; {\rm m}` is the change in the position of this sprinter during that part of the run.

Substitute in these values into the expression for acceleration:

`\begin{aligned}a &= ((11.5)^(2) - (0)^(2))/(2\, (19.0))\; {\rm m\cdot s^(-2)} \\ &\approx 3.48\; {\rm m\cdot s^(-2)}\end{aligned}`.

In other words, the acceleration of this sprinter would be approximately
`3.48\; {\rm m\cdot s^(-2)}` under the assumptions.