A simple model for a person running a 100m race is to assume the sprinter runs with constant acceleration until reaching top speed, and then maintains that speed through the finish line. If a sprinter reaches their top speed of 11.2ms-1 in 2.15s, what will be their total time?

a simple model for a person running the 100m dash is to assume the sprinter runs with the constant acceleration until reaching top speed, then maintains that speed through the finish line. if a sprinter reaches his top speed of 11.2 m/s in 2.14 s, what will be his total time

Well, assuming the sprinter maintains their top speed of 11.2 m/s through the finish line, their total time can be calculated by adding the time it took to reach top speed to the time it takes to cover the remaining distance at that speed. So, let's do some math with a twist!

First, let's find out how far our sprinter travels during the acceleration phase. Using the equation of motion: s = u*t + 0.5*a*t^2, where s is distance, u is initial velocity, t is time, and a is acceleration, we can rearrange the equation and plug in the values we know.

In this case, the initial velocity (u) is 0 m/s because the sprinter starts from rest. The acceleration (a) can be calculated by dividing the final velocity (v = 11.2 m/s) by the time (t = 2.15 s). So, the distance during the acceleration phase is as follows:

s = 0.5*a*t^2
s = 0.5*(11.2 m/s / 2.15 s)*(2.15 s)^2
s = 0.5*(11.2 m/s)*(2.15 s)
s ≈ 12.064 m (rounded to three decimal places for the sake of accuracy)

Now that we know the distance covered during the acceleration phase, let's determine the time it takes to cover the remaining distance at top speed. The remaining distance is 100 m - 12.064 m, which is approximately 87.936 m.

Using the equation: t = s/v, where t is time, s is distance, and v is velocity, we get:

t = (87.936 m) / (11.2 m/s)
t ≈ 7.849 s (rounded to three decimal places because we're feeling fancy)

Now, let's add the time for the acceleration phase to the time for the remaining distance:

Total time = 2.15 s + 7.849 s
Total time ≈ 9.999 s

So, according to our simple model, the sprinter will finish the 100m race in approximately 9.999 seconds. Let's hope they don't trip over their speed demon shoelaces!

To find the total time taken by the sprinter to complete the 100m race, we need to calculate the time it takes to reach the top speed and then add it to the time it takes to cover the remaining distance at the top speed.

Given:
Initial velocity (u) = 0 ms^(-1) (since the sprinter starts from rest)
Final velocity (v) = 11.2 ms^(-1)
Time taken to reach the top speed (t1) = 2.15 s
Distance covered during acceleration (s1) = ?

To find the distance covered during acceleration (s1), we can use the formula:

s = ut + (1/2)at^2

Since the initial velocity (u) is 0, the formula simplifies to:

s = (1/2)at^2

where:
s = distance covered during acceleration
a = acceleration
t = time taken to reach the top speed

Substituting the values, we get:

s1 = (1/2) * a * t1^2

Now, since the acceleration (a) is constant throughout the race, we can calculate it using the equation:

a = (v - u) / t1

where:
a = acceleration
v = final velocity
u = initial velocity
t1 = time taken to reach the top speed

Substituting the given values, we get:

a = (11.2 ms^(-1) - 0 ms^(-1)) / 2.15 s

Now that we have calculated the acceleration, we can substitute it back into the formula to find s1.

s1 = (1/2) * (11.2 ms^(-1) - 0 ms^(-1)) / 2.15 s * 2.15 s^2

Next, we need to find the remaining distance (s2) that the sprinter has to cover at the top speed. Since the top speed is maintained, the acceleration is 0 during this period. Therefore, we can simply calculate s2 using the formula:

s2 = 100 m - s1

Finally, we can calculate the time taken to cover the remaining distance at the top speed (t2) using the formula:

t2 = s2 / v

where:
t2 = time taken to cover the remaining distance
s2 = remaining distance to cover
v = final velocity

Once we have t1 and t2, we can find the total time (t_total) by adding them together:

t_total = t1 + t2

By following this method, you can calculate the total time taken by the sprinter to complete the 100m race.

the acceleration is

a = 11.2m/s / 2.15s = 5.21m/s^2

during the 2.15s, the distance

s = 1/2 at^2 = 1/2 (5.21)(2.15^2) = 12.04m

so, the runner runs
12.04m in 2.15s
87.96m at 11.2m/s = 7.85s

total time is thus 10.00s