Question

A pair of runners, A and B, are running on separate paths towards point 2 in the image. On both paths, point 1 is the same horizontal distance from point 2. The runners start and end at the same time on their respective paths. Which of the following is true about the runners' average speed and velocity? Select ALL that apply.

A. Both runners have the same velocity since they covered the same distance on the same amount of time.
B. Runner A has a greater speed since a greater distance was covered in the same amount of time
C. Runner B has a greater speed since a greater distance was covered in the same amount of time
D. Runner A has a greater velocity since the total displacement was greater than runner B
E. Runner B has greater velocity since the total displacement was greater than runner A

Answer 1

Answer:

C. Runner B has a greater speed since a greater distance was covered in the same amount of time.

Explanation:

Given information:

The time taken by both the runners A and B is same.

The horizontal distance (shortest distance or displacement) between point 1 and 2 is equal in both the paths.

From the given figure, the distance between point 1 and 2 in path B is more than that in path A.

Average velocity is the ratio of change in displacement with time and average speed is the ratio of total distance covered with time.

Now, the displacement between point 1 and 2 in both the paths is equal. and hence, the average velocity will also be same.

Average speed of runner B will be more as the distance covered by B is more then that by A.

Therefore, option C. Runner B has a greater speed since a greater distance was covered in the same amount of time is correct.

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Answer 2

The difference between vectors and scalars allows us to find that the correct answers are:

A.  Both runners have the same velocity since they covered the same distance on the same amount of time

C. Runner B has a greater speed since a greater distance was covered in the same amount of time

Kinematics studies the movement of bodies, finding relationships between the position, velocity and acceleration of bodies

In general, the magnitudes of kinematics are vectors, which is why they have modulus and direction, therefore vector algebra must be used to perform the sum.

              v = $\frac{\Delta s}{\Delta t}$

The bold letters indicate vectors, v is the velocity, Δs the displacement (vector) and Δt the time (scalar)

In some cases scalar magnitudes are used, in kinematics they are given a different name: distance and speed.

              v = $\frac{\Delta s}{\Delta t}$

Where v is the speed, Δs the distance (scalar) and Δt the time (scalar)

This problem shows the difference between the two types of quantities  

Let's look for the velocity of each runner.

They indicate that both leave point 1 and arrive at point 2, regardless of the intermediate paths, the displacement is the same.

They indicate that they arrive at the same time

          v = $\frac{\Delta s}{\Delta t}$

           

Consequently the velocity is the same for the two runners.

Let's look for speed

From the graph the distance of corridor B is greater than the distance traveled by corridor A

They indicate that the two arrive at the same time

           $v_a = \frac{\Delta x_a}{ \Delta t}$

           $v_b = \frac{\Delta x_b}{ \Delta t}$            

           $v_a > v_b$

Let's analyze the different statements

A. True. Vector velocity is the same for both runners

B. False. The speed of corridor a is less

C. True. The speed of runner A is greater than the speed of runner B

D. False. Speed ​​are equal

E. False The speed is the same.

In conclusion with the difference between vectors and scalars we can find that the correct answers are:

A.  Both runners have the same velocity since they covered the same distance on the same amount of time

C. Runner B has a greater speed since a greater distance was covered in the same amount of time

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