One simple model for a person running the 100 m dash is to assume the sprinter runs with constant acceleration until reaching top speed, then maintains that speed through the finish line.

If a sprinter reaches his top speed of 10.8 m/s in 2.54 s, what will be his total time?

While accelerating, he runs 5.4*2.54 = 13.72 meters. (The average speed is half the maximum).

That leaves 86.28 m still to be run at 10.8 m/s. That will take 10.8/10.8 = 7.99 s.

The total time for the 100 meters is
7.99 + 2.54 = 10.53 s

To find the total time, we need to break down the problem into two parts: the time taken to reach top speed and the time taken to cover the remaining distance at top speed.

First, let's calculate the time taken to reach top speed. We are given the initial velocity (0 m/s) and the final velocity (10.8 m/s), and we need to find the acceleration. We can use the formula:

final velocity = initial velocity + (acceleration * time)

Rearranging the formula, we get:

acceleration = (final velocity - initial velocity) / time

Plugging in the values, we have:

acceleration = (10.8 m/s - 0 m/s) / 2.54 s

Simplifying,

acceleration = 4.25 m/s²

Now that we have the acceleration, we can find the time taken to reach top speed using the formula:

time = (final velocity - initial velocity) / acceleration

Plugging in the values, we get:

time = (10.8 m/s - 0 m/s) / 4.25 m/s²

Simplifying,

time = 2.54 s

So, the time taken to reach top speed is 2.54 seconds.

Next, we need to find the time taken to cover the remaining distance at top speed. We are not given the distance, but it is safe to assume that the remaining distance is 100 meters (as mentioned in the question).

Since the sprinter maintains a constant speed of 10.8 m/s, we can divide the distance by the speed to find the time taken:

time = distance / speed

Plugging in the values,

time = 100 m / 10.8 m/s

Simplifying,

time ≈ 9.26 s

Therefore, the time taken to cover the remaining distance at top speed is approximately 9.26 seconds.

To find the total time, we add the time taken to reach top speed (2.54 s) and the time taken to cover the remaining distance (9.26 s):

total time = 2.54 s + 9.26 s

total time ≈ 11.8 s

Hence, the sprinter's total time to run the 100 m dash is approximately 11.8 seconds.

To calculate the total time, we need to determine the time it takes for the sprinter to reach their top speed and the time it takes for them to run the distance at that top speed.

1. Time to reach top speed:
We are given that the sprinter reaches a top speed of 10.8 m/s in 2.54 seconds. This means the acceleration can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
acceleration = (10.8 m/s - 0 m/s) / 2.54 s
acceleration = 4.25 m/s^2

2. Time to maintain top speed:
Since the sprinter maintains their top speed through the finish line, we can assume their acceleration is zero during this time. Therefore, the time it takes to run the distance at the top speed is given by:
time = distance / speed

3. Total time:
The total time is the sum of the time to accelerate to top speed and the time to maintain the top speed. Let's assume the distance of the 100 m dash.

speed = 10.8 m/s
distance = 100 m

time to maintain top speed = distance / speed
time to maintain top speed = 100 m / 10.8 m/s
time to maintain top speed ≈ 9.259 s

total time = time to reach top speed + time to maintain top speed
total time = 2.54 s + 9.259 s
total time ≈ 11.799 s

Therefore, the total time for the sprinter to complete the 100 m dash is approximately 11.799 seconds.