Question

having problems staying logged in or are you experiencing issues? please visit our troubleshooting section for solutions. consider the dot diagrams for objects a, b, and c. the arrow represents the direction of motion. match the motion of objects a, b, and c to one of the lines on the graph. numbers can be used only one time. a dot diagram with four red dots, arrow left, b dot diagram with five red dots, arrow left, c dot diagram with nine red dots, arrow right. a matches graph: blank, b matches graph: blank, c matches graph: blank. top graph: posn (y-axis) vs t (x-axis) with lines 1, 2, 3 (increasing). bottom graph: posn (y-axis) vs t (x-axis) with lines 4, 5, 6 (decreasing). student name: redacted, level: dots and graphs, progress report with #1, #2, #3 (yellow), #4 (red). buttons: tap for question-specific help, help me!, view directions, to main menu.

Explanation:

To solve this, we analyze the dot diagrams (motion) and match to position - time graphs:

Step 1: Analyze Object A

• The dot diagram for A has dots spaced with increasing distance (since the arrow is left, but spacing: first dot, then a gap, then a dot, etc. Wait, actually, for motion: if the arrow is left, it's moving left (decreasing position over time). But the spacing: let's see the dots. For A, the dots are more spread out as we go left? Wait, no, the direction of motion is left (arrow). So as time (number of dots, since each dot is a time interval) increases, position decreases. Now, the spacing between dots: the first dot, then a dot, then a dot, then a dot. Wait, the spacing between the dots (time intervals) for A: the distance between consecutive dots (in position) is increasing? Wait, no, let's think about speed. The steeper the line in position - time graph (for decreasing position, lower graph), the faster the speed. For A, the dots are spaced with larger gaps (so faster speed, since in same time, more distance covered). So in the lower graphs (position decreasing with time), the steepest line (most negative slope) would be for the fastest speed. Wait, no: in position - time graphs, slope is velocity. For motion to the left (decreasing position), slope is negative. The steeper the negative slope, the faster the speed (more distance covered per time).

Looking at Object A's dot diagram: the dots are spaced such that the distance between consecutive dots (in position) is large (so fast speed). So in the lower graphs (position vs time, decreasing), the steepest line (like graph 6) would be for A? Wait, no, maybe I got the direction wrong. Wait, the upper graphs are position increasing with time (motion to the right), lower are position decreasing (motion to the left).

Wait, Object A: arrow is left (motion to left, position decreases over time). The dots: let's count the number of dots and their spacing. For A: dots are at positions (let's assume) with large gaps. So time between dots is same (each dot is a time step), so distance covered per time step is large (fast speed). So in the lower graphs (position - time, decreasing), the steepest line (most negative slope) is graph 6? Wait, no, maybe:

Wait, Object C: arrow is right (motion to right, position increases over time). The dot diagram for C has dots very close together (small spacing), so slow speed (small distance per time step). So in upper graphs (position increasing), the least steep line (graph 3) would be for C.

Object B: arrow is left (motion to left, position decreases). Dots are more closely spaced than A (so slower speed than A, faster than C? Wait, no, B's dots: let's see, B has 5 dots, spaced more closely than A (A has 4 dots, more spread out). So B's speed is slower than A (since in same time, less distance covered). So in lower graphs (position - time, decreasing), B would have a less steep slope than A. So A (fast left) → graph 6, B (slower left) → graph 5, C (slow right) → graph 3? Wait, no, upper graphs: 1,2,3 (position increasing, right motion). Lower: 4,5,6 (position decreasing, left motion).

Wait, let's re - express:

• Object C: Motion to the right (arrow right), dots are very close (small distance per time → slow speed). So in upper graphs (position vs time, increasing), the least steep line (smallest slope) is graph 3. So C matches graph 3.

• Object A: Motion to the left (arrow left), dots are spread out (large distance per time → fast speed). In lower graphs (position vs time, decreasing), the steepest line (largest negative slope…

Step1: Analyze Object C (Right Motion)

Object C moves right (arrow right). Its dot diagram has closely - spaced dots (small distance per time step, slow speed). In position - time graphs with increasing position (upper graphs), the least steep line (smallest slope) is graph 3. So C matches graph 3.

Step2: Analyze Object A (Left Motion)

Object A moves left (arrow left). Its dot diagram has widely - spaced dots (large distance per time step, fast speed). In position - time graphs with decreasing position (lower graphs), the steepest line (largest negative slope) is graph 6. So A matches graph 6.

Step3: Analyze Object B (Left Motion)

Object B moves left (arrow left). Its dot diagram has dots spaced more closely than A (medium distance per time step, medium speed). In position - time graphs with decreasing position (lower graphs), the line with medium negative slope (between 4 and 6) is graph 5. So B matches graph 5.

Answer:

A matches graph: 6

B matches graph: 5

C matches graph: 3