Question

question 20 (1 point) what is the acceleration of the car at t=5.0 seconds? velocity vs. time graph: y-axis (velocity, m/s) with 0.0, 5.0, 10.0, 15.0; x-axis (time, s) with 0.0, 2.0, 4.0, 6.0; line from (0,0) to (4,10), then horizontal to (6,10) options: a 2.5m/s/s, b 3m/s/s, c 0.0m/s/s, d 2.0m/s/s

Explanation:

Step1: Recall acceleration from velocity - time graph

Acceleration is the slope of the velocity - time graph. For a velocity - time graph, when the graph is a horizontal line (constant velocity), the slope (acceleration) is 0 because \(a=\frac{\Delta v}{\Delta t}\) and \(\Delta v = 0\) for constant velocity.

Looking at the velocity - time graph, at \(t = 5.0\) seconds, the velocity - time graph is a horizontal line (from \(t = 4.0\) s to \(t=6.0\) s, velocity is constant at \(10.0\) m/s). So, \(\Delta v=v_{final}-v_{initial}\), and since \(v_{final}=v_{initial} = 10.0\) m/s (constant), \(\Delta v = 0\). Then \(a=\frac{\Delta v}{\Delta t}=\frac{0}{\Delta t}=0\) m/s² (where \(\Delta t\) is non - zero, but the numerator is zero).

Answer:

c. 0.0m/s/s