Question

3 maya is analyzing the motion of two cars, a and b, moving along a straight road. the diagram shows their positions at one - second intervals. based on this information, what can maya conclude about the cars speeds and velocities? a. car a has a higher speed and velocity than car b. b. car a and car b have the same speed, but different velocities. c. car b has a higher speed than car a, but they have the same direction. d. car a and car b have the same velocity, but different directions. 4 nathan is analyzing data from a gps tracker attached to a cyclist. the table shows the cyclists position along a straight road at different times. what can nathan conclude about the cyclists motion based on this data? time (s) position (m) 0 0 5 20 10 40 15 60 20 80 a. the cyclist has a constant speed of 4 m/s and a constant velocity of 4 m/s in the positive direction. b. the cyclist has a constant speed of 20 m/s, but the velocity cannot be determined without knowing the direction. c. the cyclist has a constant speed of 4 m/s and a constant velocity of 4 m/s in the negative direction.

Explanation:

Step1: Recall speed and velocity formulas

Speed $v = \frac{\Delta x}{\Delta t}$, velocity is speed with direction.

Step2: Analyze cyclist data

For the cyclist, from $t = 0\ s$ to $t=5\ s$, $\Delta x=20 - 0=20\ m$, $\Delta t = 5-0 = 5\ s$, $v=\frac{20}{5}=4\ m/s$.
From $t = 5\ s$ to $t = 10\ s$, $\Delta x=40 - 20=20\ m$, $\Delta t=10 - 5=5\ s$, $v=\frac{20}{5}=4\ m/s$.
From $t = 10\ s$ to $t = 15\ s$, $\Delta x=60 - 40=20\ m$, $\Delta t=15 - 10=5\ s$, $v=\frac{20}{5}=4\ m/s$.
From $t = 15\ s$ to $t = 20\ s$, $\Delta x=80 - 60=20\ m$, $\Delta t=20 - 15=5\ s$, $v=\frac{20}{5}=4\ m/s$.
Since position is increasing with time, the direction is positive. So speed is $4\ m/s$ and velocity is $4\ m/s$ in positive direction.

Answer:

A. The cyclist has a constant speed of 4 m/s and a constant velocity of 4 m/s in the positive direction.