Question

3 multiple choice 0.5 points
which sketch is the velocity vs time graph corresponding to the position vs time graph given.
options:
c
d
b
a

Explanation:

Step1: Analyze segment A-B

Velocity is slope of $x(t)$: $\frac{1.5-4}{1-0}=-2.5$ (negative constant)

Step2: Analyze segment B-C

Velocity is slope of $x(t)$: $\frac{1.5-1.5}{3-1}=0$ (zero constant)

Step3: Analyze segment C-D

Velocity is slope of $x(t)$: $\frac{2-1.5}{5-3}=0.25$ (positive small constant)

Step4: Analyze segment D-E

Velocity is slope of $x(t)$: $\frac{5-2}{6-5}=3$ (positive large constant)

Step5: Analyze segment E-end

Velocity is slope of $x(t)$: $\frac{5-5}{t>6}=0$ (zero constant)

Step6: Match to options

Only option C has negative constant, zero, small positive constant, large positive constant, zero velocity segments in order.

Answer:

C. The velocity vs time graph matching the position vs time graph's slope changes