Question

the chart shows the time, initial velocity, and final velocity of three riders.

rider	time	initial velocity	final velocity
franklin	8.5 sec	50	50
kendall	6 sec	53.2	67

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:

Step1: Calculate acceleration for each rider

The formula for acceleration is \(a=\frac{v - u}{t}\), where \(v\) is final velocity, \(u\) is initial velocity, and \(t\) is time.
For Kendall: \(a_{Kendall}=\frac{67 - 53.2}{6}=\frac{13.8}{6}=2.3\)
For Franklin: \(a_{Franklin}=\frac{50 - 50}{8.5}=0\)
For Gabriella: \(a_{Gabriella}=\frac{32 - 55}{10}=\frac{- 23}{10}=-2.3\)

Step2: Analyze the results

Kendall has a positive acceleration (\(a = 2.3\)), which means she is speeding up.
Franklin has an acceleration of \(a = 0\), which means he is not accelerating.
Gabriella has a negative acceleration (\(a=-2.3\)), which means she is slowing down.

Answer:

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