Question

roger and natalie travel in similar cars. rogers car drives the two miles to school in 7.5 minutes. natalie drives the same distance in the opposite direction but in only 6.5 minutes. what is true of their velocities? a roger and natalie have velocities with the same magnitude only. b natalies velocity is greater in magnitude than rogers velocity. c rogers velocity is greater in magnitude than natalies velocity. d roger and natalie have velocities with the same direction and magnitude.

Explanation:

Step1: Recall velocity formula

Velocity $v=\frac{d}{t}$, where $d$ is distance and $t$ is time. Given Roger drives 2 miles in 7.5 minutes, his speed $v_{R}=\frac{2}{7.5}$ miles per minute. Natalie drives 2 miles in 6.5 minutes, her speed $v_{N}=\frac{2}{6.5}$ miles per minute.

Step2: Compare magnitudes

Since $\frac{2}{6.5}>\frac{2}{7.5}$, Natalie's speed (magnitude of velocity) is greater than Roger's. And they travel in opposite - directions. Velocity is a vector with magnitude and direction.

Answer:

C. Natalie's velocity is greater in magnitude than Roger's velocity.