Question

by how much does the velocity change b? (delta v from the before and after values of velocity at that point)
options: 0 m/s, -1.67 m/s, +1.67 m/s, +1 m/s

Explanation:

Step1: Find velocity before point B

Velocity is slope of x-t graph: $v_{\text{before}} = \frac{x_B - x_A}{t_B - t_A} = \frac{1.5 - 4}{1.5 - 0} = \frac{-2.5}{1.5} = -\frac{5}{3} \approx -1.67$ m/h

Step2: Find velocity after point B

Velocity is slope of x-t graph: $v_{\text{after}} = \frac{x_C - x_B}{t_C - t_B} = \frac{1.5 - 1.5}{3 - 1.5} = 0$ m/h

Step3: Calculate velocity change

$\Delta v = v_{\text{after}} - v_{\text{before}} = 0 - (-\frac{5}{3}) = +\frac{5}{3} \approx +1.67$ m/h
(Note: Unit correction: the graph uses hours, but options use m/s; assuming this is a unit typo in the question, the magnitude and sign match the option.)

Answer:

+1.67 m/s