An Olympic athlete wants to complete the 4000-m run in less than 12.0 minutes. After exactly 10.0 minutes of running at a constant speed, she still has 800 m to go. If she then accelerates at a rate of 0.40 m/ s 2 , a) how much longer will it take her to complete the race?

Answer 1

Let's break down the information given:
- The athlete wants to complete the 4000-m run in less than 12.0 minutes.
- After 10.0 minutes of running at a constant speed, she still has 800m to go.
- She accelerates at a rate of 0.40 m/s^2.

To find out how much longer it will take her to complete the race, we need to calculate the time it takes for her to cover the remaining distance of 800m.

Using the equation for calculating distance with constant acceleration:

\[d = ut + \frac{1}{2} a t^2\]

where:
d = distance covered
u = initial speed
t = time taken
a = acceleration

We know that u = 0 m/s (since she started accelerating after 10.0 minutes), a = 0.40 m/s^2, and d = 800m. Let's rearrange the formula to solve for t:

\[d = \frac{1}{2} a t^2\]
\[800 = \frac{1}{2} \cdot 0.40 \cdot t^2\]
\[1600 = 0.20 \cdot t^2\]
\[t^2 = \frac{1600}{0.20}\]
\[t^2 = 8000\]
\[t = \sqrt{8000}\]
\[t \approx 89.44\]

So, it will take her approximately 89.44 seconds longer to complete the race.

Answer 2

b) will she achieve her desired time?