Question

3 maya is analyzing the motion of two cars, a and b, traveling 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? 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:

Question 3

Step1: Calculate speed of Car A

Speed = distance/time. For Car A, distance between consecutive points is 2 cm and time - interval is 1 s. So speed of Car A, $v_A=\frac{2\ cm}{1\ s}=2\ cm/s$.

Step2: Calculate speed of Car B

For Car B, distance between consecutive points is 3 cm and time - interval is 1 s. So speed of Car B, $v_B = \frac{3\ cm}{1\ s}=3\ cm/s$.

Step3: Analyze direction and velocity

Both cars are moving in the same direction (right - hand side as per the diagram). Velocity is speed with direction. Since $v_B>v_A$ and direction is the same for both.

Step1: Calculate speed

Speed $v=\frac{\Delta x}{\Delta t}$. For example, from $t = 0$ s to $t = 5$ s, $\Delta x=20 - 0=20$ m and $\Delta t = 5-0 = 5$ s, $v=\frac{20\ m}{5\ s}=4$ m/s. Checking for other time - intervals: from $t = 5$ s to $t = 10$ s, $\Delta x=40 - 20 = 20$ m, $\Delta t=10 - 5=5$ s, $v=\frac{20\ m}{5\ s}=4$ m/s. Since position is increasing with time, the direction is positive. Velocity has the same magnitude as speed (4 m/s) and is in the positive direction.

Answer:

C. Car B has a higher speed than Car A, but they have the same direction.

Question 4