Question

apply it

1. sep interpret the data table records the motion of a toy car moving across a floor. the first two columns record positions and corresponding times. the third and fourth columns record speed and velocity for the four 1 - meter distances. some speed and velocity data are missing. complete the table. then explain how to calculate average speed and velocity.

position|time|speed in interval|velocity in interval
0 m east|0 s| - | -
1 m east|1 s| - | -
2 m east|2 s|1 m/s|1 m/s east
3 m east|4 s| - |2 m/s east
4 m east|8 s|0.5 m/s|0.5 m/s east
0.25 m/s

1. illustrate draw a diagram of the path the car took. add labels to show how the cars speed and velocity changed. label where and when the car had uniform motion. write a caption comparing the velocity and speed of the car in terms of distance, displacement, and direction.

Explanation:

Step1: Recall speed formula

Speed $v=\frac{d}{t}$, where $d$ is distance and $t$ is time. For the first - interval from 0 m to 1 m in 1 s, $v=\frac{1 - 0}{1 - 0}=1$ m/s.

Step2: Recall velocity concept

Velocity is a vector. Since the motion is in a straight - line (east - direction) and speed is 1 m/s for the first interval, velocity is 1 m/s east.

Step3: Calculate speed for second interval

From 1 m to 2 m in $2 - 1 = 1$ s. Speed $v=\frac{2 - 1}{2 - 1}=1$ m/s. Since direction is east, velocity is 1 m/s east.

Step4: Calculate speed for third interval

From 2 m to 3 m in $4 - 2 = 2$ s. Speed $v=\frac{3 - 2}{4 - 2}=0.5$ m/s. Since direction is east, velocity is 0.5 m/s east.

Step5: Calculate speed for fourth interval

From 3 m to 4 m in $8 - 4 = 4$ s. Speed $v=\frac{4 - 3}{8 - 4}=0.25$ m/s. Since direction is east, velocity is 0.25 m/s east.

Step6: Calculate average speed

Total distance $d_{total}=4$ m, total time $t_{total}=8$ s. Average speed $v_{avg}=\frac{d_{total}}{t_{total}}=\frac{4}{8}=0.5$ m/s.

Step7: Calculate average velocity

Displacement $\Delta x = 4$ m east, total time $t_{total}=8$ s. Average velocity $\vec{v}_{avg}=\frac{\Delta x}{t_{total}} = 0.5$ m/s east.

Answer:

Average speed: 0.5 m/s
Average velocity: 0.5 m/s east