Question

1. mandy and eve are traveling to their sister kristins house.

a. who lives closer to kristin?
b. who is traveling at a faster speed?
c. what speed are mandy and eve traveling at?

1. ross is drag racing his sisters porsche.

a. describe the motion of the car
b. is the car speeding up or slowing down?

Explanation:

Step1: Analyze starting - point for distance

The initial position on the position - time graph represents the starting distance from Kristin's house. Mandy starts at a position of 1 km and Eve starts at 0 km. So Eve starts closer to Kristin.

Step2: Analyze slope for speed comparison

The slope of a position - time graph gives the speed. The steeper the slope, the faster the speed. Mandy's line has a steeper slope than Eve's, so Mandy is traveling faster.

Step3: Calculate Mandy's speed

The slope formula is $m=\frac{\Delta y}{\Delta x}$. For Mandy, $\Delta y = 3 - 1=2$ km and $\Delta x = 15$ min. So Mandy's speed $v_M=\frac{2}{15}\text{ km/min}\approx0.133\text{ km/min}$.

Step4: Calculate Eve's speed

For Eve, $\Delta y = 3 - 0 = 3$ km and $\Delta x = 20$ min. So Eve's speed $v_E=\frac{3}{20}= 0.15\text{ km/min}$.

For question 6:

Step5: Describe Ross's car motion

The position - time graph of Ross's car shows a non - linear curve. The car starts from rest (starts at the origin) and moves forward as time increases.

Step6: Determine acceleration

The slope of the position - time graph is increasing. Since the slope represents speed and the slope is getting steeper over time, the car is speeding up.

Answer:

5a. Eve
5b. Mandy
5c. Mandy's speed is $\frac{2}{15}\text{ km/min}\approx0.133\text{ km/min}$, Eve's speed is $\frac{3}{20}=0.15\text{ km/min}$
6a. The car starts from rest and moves forward.
6b. The car is speeding up.