Question

the graph represents velocity over time.
what is the acceleration?
○ -0.4 m/s²
○ -0.2 m/s²
○ 0.2 m/s²
○ 0.4 m/s²

Explanation:

Step1: Recall the formula for acceleration

Acceleration \(a=\frac{\Delta v}{\Delta t}\), where \(\Delta v\) is the change in velocity and \(\Delta t\) is the change in time.

Step2: Identify two points on the graph

Let's take the initial point \((t_1 = 2\space s,v_1=0\space m/s)\) and the point \((t_2 = 102\space s,v_2=- 40\space m/s)\)

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

\(\Delta v=v_2 - v_1=-40 - 0=-40\space m/s\)
\(\Delta t=t_2 - t_1=102 - 2 = 100\space s\)

Step4: Calculate acceleration

\(a=\frac{\Delta v}{\Delta t}=\frac{-40}{100}=- 0.4\space m/s^{2}\)

Answer:

\(-0.4\space m/s^{2}\)