Question

the chart shows the time, initial velocity, and final velocity of three riders. 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 determine the riders' accelerations (or lack thereof), we calculate acceleration using the formula \( a = \frac{v_f - v_i}{t} \), where \( v_f \) is final velocity, \( v_i \) is initial velocity, and \( t \) is time.

• Gabriella: \( a = \frac{32 - 55}{10} = \frac{-23}{10} = -2.3 \) (negative acceleration means slowing down).
• Franklin: \( a = \frac{50 - 50}{8.5} = \frac{0}{8.5} = 0 \) (no acceleration, velocity is constant).
• Kendall: \( a = \frac{67 - 53.2}{6} = \frac{13.8}{6} = 2.3 \) (positive acceleration means speeding up).

Gabriella’s magnitude of acceleration (2.3) matches Kendall’s (2.3), with Gabriella slowing down and Kendall speeding up. Franklin has no acceleration.

Answer:

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