Question

the chart shows the time, initial velocity, and final velocity of three riders.
rider\ttime\tinitial velocity\tfinal velocity
gabriella\t10 sec\t55\t32
franklin\t8.5 sec\t50\t50
kendall\t6 sec\t53.2\t67
which best describes the riders’ final velocities ?
○ gabriella is speeding up at the same rate that kendall is slowing down, and franklin is not accelerating.
○ gabriella is slowing down at the same rate that kendall is speeding up, and franklin is not accelerating.
○ gabriella and franklin are both slowing down, and kendall is accelerating.
○ gabriella is slowing down, and kendall and franklin are accelerating.

Explanation:

To solve this, we calculate the acceleration (change in velocity over time) for each rider. Acceleration formula: \( a = \frac{v_f - v_i}{t} \)

Step 1: Calculate Gabriella's acceleration

• Initial velocity (\( v_i \)) = 55, Final velocity (\( v_f \)) = 32, Time (\( t \)) = 10 sec

\( a_{Gabriella} = \frac{32 - 55}{10} = \frac{-23}{10} = -2.3 \) (negative means slowing down)

Step 2: Calculate Franklin's acceleration

• \( v_i = 50 \), \( v_f = 50 \), \( t = 8.5 \) sec

\( a_{Franklin} = \frac{50 - 50}{8.5} = \frac{0}{8.5} = 0 \) (no acceleration)

Step 3: Calculate Kendall's acceleration

• \( v_i = 53.2 \), \( v_f = 67 \), \( t = 6 \) sec

\( a_{Kendall} = \frac{67 - 53.2}{6} = \frac{13.8}{6} = 2.3 \) (positive means speeding up)

Now, analyze the options:

• Gabriella’s acceleration magnitude: \( |-2.3| = 2.3 \) (slowing down).
• Kendall’s acceleration: \( 2.3 \) (speeding up).
• Franklin’s acceleration: \( 0 \) (not accelerating).

This matches the second option: Gabriella is slowing down at the same rate that Kendall is speeding up, and Franklin is not accelerating.

Answer:

Gabriella is slowing down at the same rate that Kendall is speeding up, and Franklin is not accelerating.