Question

an experimenter records data for the speed and time of rolling carts traveling along a track. the table shows the data for four trials. use this table for questions 2 - 3.

1. in which trial did the cart experience the greatest average acceleration?

a. trial 2 c. trial 4
b. trial 3 d. trial 1

Explanation:

Step1: Recall the formula for average acceleration

The formula for average acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v = v_{final}-v_{initial}\) and \(\Delta t=t_{final} - t_{initial}\).

Step2: Calculate acceleration for each trial

• Trial 1:

\(v_{initial}=2\ m/s\), \(v_{final}=15\ m/s\), \(t_{initial} = 0\ s\), \(t_{final}=3\ s\)
\(\Delta v=15 - 2=13\ m/s\), \(\Delta t=3-0 = 3\ s\)
\(a_1=\frac{13}{3}\approx4.33\ m/s^{2}\)

• Trial 2:

\(v_{initial}=4\ m/s\), \(v_{final}=4\ m/s\), \(\Delta v=4 - 4=0\ m/s\)
\(a_2=\frac{0}{\Delta t}=0\ m/s^{2}\)

• Trial 3:

\(v_{initial}=10\ m/s\), \(v_{final}=7\ m/s\), \(\Delta v=7 - 10=- 3\ m/s\)
\(\Delta t=3 - 0=3\ s\)
\(a_3=\frac{-3}{3}=-1\ m/s^{2}\)

• Trial 4:

\(v_{initial}=1\ m/s\), \(v_{final}=25\ m/s\), \(\Delta v=25 - 1=24\ m/s\)
\(\Delta t=3 - 0=3\ s\)
\(a_4=\frac{24}{3}=8\ m/s^{2}\)

Answer:

\(d\) (trial 1 has an acceleration of approximately \(4.33\ m/s^{2}\), trial 2 has \(0\ m/s^{2}\), trial 3 has \(- 1\ m/s^{2}\), trial 4 has \(8\ m/s^{2}\), so trial 4 has the greatest average acceleration)