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:

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

Step 1: Calculate Gabriella's acceleration

\(v_i = 55\), \(v_f = 32\), \(t = 10\) sec.
\(a=\frac{32 - 55}{10}=\frac{-23}{10}=-2.3\) (negative means slowing down).

Step 2: Calculate Franklin's acceleration

\(v_i = 50\), \(v_f = 50\), \(t = 8.5\) sec.
\(a=\frac{50 - 50}{8.5}=\frac{0}{8.5}=0\) (no acceleration).

Step 3: Calculate Kendall's acceleration

\(v_i = 53.2\), \(v_f = 67\), \(t = 6\) sec.
\(a=\frac{67 - 53.2}{6}=\frac{13.8}{6}=2.3\) (positive means speeding up).

Now, analyze the options:

• Gabriella's acceleration magnitude: \(2.3\) (slowing down), Kendall's: \(2.3\) (speeding up), Franklin: \(0\) (no acceleration). This matches the second option.

Answer:

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