Ken wishes to get produce from the store, which is a distance D = 2.5 km east of his condo. Ken rides his bike to the store at a constant speed of v1 = 6.1 m/s, and rides back to his condo at the slower speed of v2 = 2.4 m/s.

1. how long (in second) does it take for Steve to reach the store?

2. in second, how long does the whole trip take?

3. how Long does the trip take in minutes?

4. how much distance, in kilometers, did Steve travel during the whole trip?

5. what is the magnitude of Steve's displacement, in km, for the entire trip?

6. what is the direction of Steve's displacement for the entire trip?

1. It takes Steve (or was it Ken?) 410 s to reach the store.

2. The whole trip takes Ken 1452 s.

3. In minutes, the whole trip takes 24 min.

4. Ken travels 5 km during the whole trip.

5. The magnitude of Ken's displacement is zero.

6. Since the displacement is equal to the null vector, it has no direction.

Explanation:

Hi there!

1. Using the equation of traveled distance, we can find the time it takes Ken to travel to the store:

D = v · t

Where:

D = traveled distance.

v = speed.

t = time.

Solving for t:

D/v = t

2500 m / 6.1 m/s = t

t = 410 s.

It takes Steve (or was it Ken?) 410 s to reach the store.

2. Let's find how much time it takes Ken to return home using the same equation as in part 1:

D/v = t

2500 m / 2.4 m/s = t

t = 1042 s

Then, the whole trip takes Ken (1042 s + 410 s) 1452 s.

3. In minutes, the whole trip takes (1452 / 60) 24 min.

4. Ken travels 2.5 km to reach the store and 2.5 km to return home. So, he travels (2.5 km + 2.5 km) 5 km during the whole trip.

5. The displacement (Δx) is calculated as follows:

Δx = final position - initial position

If we consider his home as the origin of the frame of reference, the store will be located at 2.5 km to east (considered the positive direction).

Since the final position and the initial position are the same (the origin of the frame of reference), the displacement is zero:

Δx = final position - initial position = 0 - 0 = 0

Another way to see it:

The displacement of Ken to the store is 2.5 km east (positive). Then, the displacement is 2.5 km west (negative). Both displacement vectors have the same magnitude but opposite direction. So, the sum of both vectors is equal to the null vector. The magnitude of the null vector is zero.

6. Since the displacement is the null vector, it has no direction.