Question

the graph shows the velocity of a bicycle as the rider moves away from a curb. based on the slope of the graph, what is the average acceleration of the bicycle? hint: slope of vt graph tells you acceleration. (4b) 0.750 m/s² 1.33 m/s² 3.00 m/s² 6.00 m/s²

Explanation:

Step1: Identify the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v = v_{final}-v_{initial}\) and \(\Delta t=t_{final}-t_{initial}\).

Step2: Determine the values from the graph

From the graph, \(v_{initial} = 8.00\ m/s\), \(v_{final}=0\ m/s\), \(t_{initial} = 0\ s\), \(t_{final}=6.00\ s\).

Step3: Calculate \(\Delta v\) and \(\Delta t\)

\(\Delta v=0 - 8.00=- 8.00\ m/s\), \(\Delta t=6.00 - 0 = 6.00\ s\).

Step4: Calculate acceleration

\(a=\frac{\Delta v}{\Delta t}=\frac{-8.00}{6.00}\approx - 1.33\ m/s^{2}\). The magnitude of acceleration (since we are asked for average acceleration, and the negative sign just indicates deceleration) is \(1.33\ m/s^{2}\).

Answer:

\(1.33\ m/s^{2}\) (corresponding to the second option in the given choices)