Question
10. Consider a football coach pacing back and forth along the sidelines. The diagram below shows several of coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the opposite direction. In other words, the coach moves from position A to B to C to D. What is the coach's average speed and average velocity?
Answer
4.4
(174 Votes)
Cecilia
Master · Tutor for 5 years
Answer
To calculate the coach's average speed and average velocity, we need to determine the total distance traveled and the total displacement, as well as the total time taken.From the picture details, we have the following positions and times:- D(-10) at 10 minutes- B(10) at 3 minutes- C(30) at 6 minutes- A(49) at 0 minutesStep 1: Calculate the total distance traveledThe coach moves from A to B to C to D, so we need to calculate the distance between each of these points.Distance from A to B: |49 - 10| = 39 unitsDistance from B to C: |10 - 30| = 20 unitsDistance from C to D: |30 - (-10)| = 40 unitsTotal distance = 39 + 20 + 40 = 99 unitsStep 2: Calculate the total displacementDisplacement is the straight-line distance from the initial position to the final position, with direction.Displacement from A to D: D - A = -10 - 49 = -59 unitsThe negative sign indicates that the displacement is in the opposite direction to the positive side of the number line.Step 3: Calculate the total time takenThe total time is the sum of all the time intervals.Total time = 10 + 3 + 6 + 0 = 19 minutesStep 4: Calculate the average speedAverage speed is the total distance traveled divided by the total time taken.Average speed = Total distance / Total timeAverage speed = 99 units / 19 minutesAverage speed ≈ 5.21 units/minuteStep 5: Calculate the average velocityAverage velocity is the total displacement divided by the total time taken.Average velocity = Total displacement / Total timeAverage velocity = -59 units / 19 minutesAverage velocity ≈ -3.11 units/minuteThe negative sign in the average velocity indicates that the overall motion of the coach is in the direction of the negative side of the number line.Final Answer:The coach's average speed is approximately 5.21 units per minute, and the coach's average velocity is approximately -3.11 units per minute.