Question

position vs. time graphs
comparing speed
position vs. time
which object moves fastest?
the object represented by line c (blue).
the object represented by line b (black).
the object represented by line a (red).

Explanation:

Step1: Recall speed formula

Speed $v = \frac{\text{Position change } \Delta x}{\text{Time change } \Delta t}$

Step2: Calculate speed for Line A

Take points $(t=4, x=5)$: $v_A = \frac{5}{4} = 1.25 \, \text{m/s}$

Step3: Calculate speed for Line B

Take points $(t=6, x=5)$: $v_B = \frac{5}{6} \approx 0.83 \, \text{m/s}$

Step4: Calculate speed for Line C

Take points $(t=4, x=5)$: $v_C = \frac{5}{10} = 0.5 \, \text{m/s}$

Step5: Compare speeds

$v_A > v_B > v_C$

Answer:

The object represented by line A (red).