Question

A cross-country runner begins a race at a standstill (v=0). At the 10-second mark, her velocity is 5.0 m/s. How far has she run in that time?

Answer 1

To determine the distance the cross-country runner covered in 10 seconds, we first calculated the acceleration and then plugged it into the displacement formula s = ½ at², giving us 25 meters.

Step-by-step explanation:

The question is asking how far a cross-country runner has traveled starting from rest and reaching a velocity of 5.0 m/s after 10 seconds. To solve this, we assume a constant acceleration and can use the kinematic equation for displacement (s), which is s = ut + ½ at2. Since the initial velocity (u) is 0, the equation simplifies to s = ½ at2. The acceleration (a) can be calculated using the formula a = (v - u) / t, where v is the final velocity and u is the initial velocity.

To find the acceleration: a = (5.0 m/s - 0 m/s) / 10 s = 0.5 m/s2.

Now, plug the acceleration and time into the displacement formula: s = ½ (0.5 m/s2) (10 s)2 = ½ (0.5) (100) m = 25 m.

Therefore, the runner has traveled a distance of 25 meters in the 10-second interval.