Question

6 which two of the following line segments show the greatest speeds?
position vs. time
□ line segment a
□ line segment c
□ line segment d
□ line segment f

Explanation:

Step1: Recall speed formula

Speed = $\frac{\text{Change in Position}}{\text{Change in Time}}$ (magnitude, since we compare speed)

Step2: Calculate speed for Segment A

Position change: $4-0=4$ m; Time change: $2-0=2$ s
Speed: $\frac{4}{2}=2$ m/s

Step3: Calculate speed for Segment C

Position change: $4-2=2$ m; Time change: $15-12=3$ s
Speed: $\frac{2}{3}\approx0.67$ m/s

Step4: Calculate speed for Segment D

Position change: $3-2=1$ m; Time change: $18-15=3$ s
Speed: $\frac{1}{3}\approx0.33$ m/s

Step5: Calculate speed for Segment F

Position change: $2-1=1$ m; Time change: $27-24=3$ s
Speed: $\frac{1}{3}\approx0.33$ m/s

Step6: Compare all speeds

$2 > 0.67 > 0.33$, so A has the highest speed, followed by C.

Answer:

Line segment A, Line segment C