Usain Bolt has achieved a top speed of 27.3 miles per hour, or 12.2 meters per second. Supposed he reached this top speed at 6 seconds into his race (finished in ). What was his acceleration at 6 seconds?
Use this equation:
The Correct Answer and Explanation is :
To find Usain Bolt’s acceleration at 6 seconds, we can use the following kinematic equation:
[
v = u + at
]
Where:
- ( v ) is the final velocity at time ( t ),
- ( u ) is the initial velocity (which we assume is 0 m/s at the start of the race),
- ( a ) is the acceleration, and
- ( t ) is the time taken.
We are given:
- ( v = 12.2 \, \text{m/s} ) (his top speed),
- ( u = 0 \, \text{m/s} ) (assuming he started from rest),
- ( t = 6 \, \text{seconds} ) (the time at which he reached his top speed).
Step 1: Plug in the values into the equation
We want to find ( a ) (acceleration). Rearranging the equation to solve for ( a ):
[
a = \frac{v – u}{t}
]
Substitute the known values:
[
a = \frac{12.2 \, \text{m/s} – 0 \, \text{m/s}}{6 \, \text{seconds}}
]
[
a = \frac{12.2}{6} = 2.0333 \, \text{m/s}^2
]
Thus, Usain Bolt’s acceleration at 6 seconds is approximately 2.03 m/s².
Explanation:
The formula used here comes from basic kinematics, where acceleration is defined as the rate of change of velocity. In the case of Usain Bolt’s race, we assume that he started from rest, which means his initial velocity ( u ) is 0. Since the top speed is reached at 6 seconds, the acceleration is simply the change in velocity divided by the time it took to reach that velocity.
In simpler terms, this means that each second, Usain Bolt’s velocity was increasing by approximately 2.03 meters per second. This high acceleration explains how an elite sprinter can rapidly reach such high speeds, achieving remarkable times in short distances.
This calculation assumes a uniform acceleration, which is a simplification, as his actual acceleration would likely have varied over the course of the race. Nonetheless, the calculated acceleration provides a good estimate for his speed at the 6-second mark of his race.