Olympic champion Justin gaitlin set a new world record for 100.0 m sprint at the last lympics by clocking 9.86 s for the race.Calculate
a)His average speed for the race
b)Assuming that he accelerated uniformly for the first 4.86 s after taking off the blocks to reach a maximum speed Vmax with which he continues for the rest of the race, is this speed likely to be same as, less than, or greater than the average speed.Why?
c)calculate the max. speed he reaches at the end of the first stage of his motion
d)Calculate the distance covered during the two stages and the steady acceleration in the first stage
Check the answer previously posted to John X for the same question
To calculate the average speed, we need to use the formula:
Average Speed = Total Distance / Total Time
a) First, we need to know the total distance covered in the 100.0 m sprint. Since it's a straight line race, the total distance is equal to 100.0 m. The total time to cover this distance is 9.86 s.
Average Speed = 100.0 m / 9.86 s
b) To determine whether the maximum speed (Vmax) is the same as, less than, or greater than the average speed, we need to understand the concept of average speed. Average speed is the total distance divided by the total time, which takes into account any variations in speed throughout the race.
In this case, Justin Gatlin accelerated uniformly for the first 4.86 s, then continued at a constant maximum speed for the remaining time. Since the average speed considers the entire duration of the race, it takes into account both the initial acceleration and the constant speed.
Therefore, the maximum speed (Vmax) is likely to be less than the average speed because the acceleration during the initial stage will be slower than the constant speed later on.
c) To calculate the maximum speed at the end of the first stage, we need to know the acceleration and the time during which the acceleration occurred. We are given that Justin Gatlin accelerated uniformly for the first 4.86 s.
First, let's calculate the acceleration using the formula:
Acceleration = Change in Velocity / Time
Assuming his initial velocity is 0 m/s:
Change in Velocity = Vmax - Initial Velocity = Vmax - 0 = Vmax
Acceleration = Vmax / 4.86 s
d) The distance covered during the two stages can be calculated using the formulas for distance, speed, and time.
For the first stage:
Distance = Initial Velocity * Time + 0.5 * Acceleration * Time^2
Since we know the initial velocity is 0 m/s and the time is 4.86 s:
Distance = 0 * 4.86 + 0.5 * (Vmax / 4.86) * (4.86)^2
The steady acceleration in the first stage is simply the acceleration calculated earlier:
Acceleration = Vmax / 4.86
For the second stage:
Distance = Speed * Time
Since the speed is constant (Vmax) and the remaining time is 9.86 s minus the time of the first stage (4.86 s):
Distance = Vmax * (9.86 - 4.86)
Note: The values of Vmax and the maximum speed he reaches at the end of the first stage cannot be determined without additional information.