Question

1. a cross - country skier moves from location a to location b, then from b to c, and then from c to d. each part of the motion takes 1 minute to complete; total time is 3 minutes. (the units are meters) a. what is the distance traveled by the skier during the 3 minutes of travel? b. what is the total displacement of the skier during the 3 minutes of travel? c. what is the displacement during the 2nd minute (from 1 to 2 minutes)? d. what is the displacement during the 3rd minute (from 2 to 3 minutes)?

Explanation:

Step1: Recall definitions

Distance is total path - length, displacement is change in position.

Step2: Analyze part a

Assume positions at each point. If we know the positions at start and end of 3 - minute interval, we can find distance. But no position values given. Let's assume positions \(x_A,x_B,x_C,x_D\). Distance \(d = |x_B - x_A|+|x_C - x_B|+|x_D - x_C|\). Without values, we can't calculate a numerical answer. But conceptually, it's sum of lengths of each part of motion.

Step3: Analyze part b

Total displacement from \(A\) to \(D\) is \(x_D - x_A\). Again, without position values, we can't calculate a number.

Step4: Analyze part c

For displacement from \(t = 1\) to \(t = 2\) minutes (from \(B\) to \(C\)), it is \(x_C - x_B\).

Step5: Analyze part d

For displacement from \(t = 2\) to \(t = 3\) minutes (from \(C\) to \(D\)), it is \(x_D - x_C\).

Since no position - value information is given in the problem statement, we can only provide general formulas. If we assume the skier moves along a straight - line and positions are \(x_1,x_2,x_3,x_4\) at times \(t = 0,1,2,3\) minutes respectively:
a. Distance \(d=x_2 - x_1+x_3 - x_2+x_4 - x_3=x_4 - x_1\) (sum of lengths of each segment)
b. Total displacement \(=x_4 - x_1\)
c. Displacement from \(t = 1\) to \(t = 2\) minutes \(=x_3 - x_2\)
d. Displacement from \(t = 2\) to \(t = 3\) minutes \(=x_4 - x_3\)

Answer:

a. General formula for distance: sum of lengths of each part of motion. Without specific position values, no numerical answer.
b. General formula for total displacement: final position - initial position. Without specific position values, no numerical answer.
c. General formula for displacement from 1 - 2 minutes: final position at 2 minutes - initial position at 1 minute. Without specific position values, no numerical answer.
d. General formula for displacement from 2 - 3 minutes: final position at 3 minutes - initial position at 2 minutes. Without specific position values, no numerical answer.