Question

mission kc5: oil drop representations
an object is moving from left to right. it’s motion is represented by the oil drop diagram at the right. this object has a ____ velocity and a ____ acceleration.
a. rightward, zero
b. leftward, zero
c. rightward, rightward
d. leftward, leftward
e. rightward, leftward
f. leftward, rightward
g. none of these
diagram: a track with red dots (oil drops) and a red arrow pointing right

Answer:

1. Velocity Direction: The object is moving from left to right, so velocity is rightward.
2. Acceleration Analysis: In an oil - drop diagram, the spacing between drops represents the distance traveled in equal time intervals. Here, the spacing between the red dots (oil drops) is increasing as the object moves from left to right. When the distance between successive positions (in equal time) increases, the object is speeding up. For an object moving rightward and speeding up, the acceleration is in the same direction as the velocity, i.e., rightward? Wait, no—wait, if the spacing is increasing, the velocity is increasing. Wait, no, let's re - examine. Wait, the oil - drop diagram: each dot is at a position at equal time intervals. If the dots are getting farther apart as it moves right, that means the object is covering more distance in each successive time interval, so its velocity is increasing. So acceleration is in the direction of motion (rightward)? Wait, no, wait, maybe I made a mistake. Wait, no—wait, if the object is moving right, and the distance between drops (time intervals) is increasing, that means the velocity is increasing (speeding up), so acceleration is rightward? But wait, let's check the options. Wait, option e is rightward, leftward. Wait, maybe I messed up. Wait, no—wait, maybe the spacing is increasing, but the direction of acceleration: if the object is moving right and the spacing between drops (time steps) is increasing, that means the velocity is increasing (because in each time step, it goes farther). So acceleration is in the direction of velocity (rightward)? But option e is rightward, leftward. Wait, maybe I got the spacing wrong. Wait, looking at the diagram: the first few dots are close, then they get farther apart. Wait, no—wait, from left to right, the dots are: first three close, then a bit more space, then more, etc. So the distance between consecutive dots (time intervals) is increasing. So velocity is increasing (since $v=\frac{\Delta x}{\Delta t}$, $\Delta t$ is constant, $\Delta x$ increasing, so $v$ increasing). So acceleration is in the direction of velocity (rightward)? But that's option c? Wait, no, wait, maybe I made a mistake. Wait, no—wait, maybe the object is moving right, but the acceleration is leftward? Wait, no, if the object is speeding up while moving right, acceleration is rightward. If it's slowing down while moving right, acceleration is leftward. Wait, let's think again. The oil - drop diagram: each dot is at time $t, t + \Delta t, t+2\Delta t$, etc. So the position of the first dot is $x_1$, second $x_2$, third $x_3$, etc. The velocity between $x_1$ and $x_2$ is $v_1=\frac{x_2 - x_1}{\Delta t}$, between $x_2$ and $x_3$ is $v_2=\frac{x_3 - x_2}{\Delta t}$, etc. If $x_3 - x_2>x_2 - x_1$, then $v_2 > v_1$, so velocity is increasing. So acceleration $a=\frac{v_2 - v_1}{\Delta t}$ is positive (same direction as velocity, which is rightward). But wait, the options: option e is rightward, leftward. Wait, maybe I misread the diagram. Wait, maybe the dots are getting closer? Wait, no, the diagram shows from left to right, the dots are: first three close, then a dot, then a bigger space, then a dot, etc. Wait, maybe the time intervals are equal, but the distance between dots is increasing, so velocity is increasing (acceleration rightward) or decreasing? Wait, no—if the distance between dots (in equal time) is increasing, velocity is increasing. So acceleration is in the direction of velocity. So the object has rightward velocity and rightward acceleration? But that's option c? Wait, no, wait the options:

a. rightward, zero (constant velocity, spacing equal)
b. leftward, zero (moving left, spacing equal)
c. rightward, rightward (speeding up right)
d. leftward, leftward (speeding up left)
e. rightward, leftward (slowing down right)
f. leftward, rightward (slowing down left)
g. none of these

Wait, looking at the diagram, the dots are spaced such that the distance between them increases as we go from left to right. So in each successive time interval, the object travels a greater distance. So velocity is increasing (since $v=\Delta x/\Delta t$, $\Delta t$ constant, $\Delta x$ increasing). So acceleration is in the same direction as velocity (rightward). So the answer should be option e? Wait, no, I'm confused. Wait, no—wait, if the object is moving right and the spacing between dots (time intervals) is increasing, that means the velocity is increasing (speeding up), so acceleration is rightward. But option e is rightward, leftward. Wait, maybe the diagram is the other way. Wait, maybe the dots are getting closer, meaning the object is slowing down. Let's re - examine the diagram: the first few dots are close, then there's a dot, then a bigger gap, then a dot, etc. Wait, no—from left to right, the first three dots are close (small $\Delta x$), then the next dot is farther (larger $\Delta x$), then the next is even farther. So $\Delta x$ is increasing, so velocity is increasing. So acceleration is rightward. So the correct option is e? No, wait, no—if velocity is increasing, acceleration is in the direction of velocity. So rightward velocity and rightward acceleration (option c). But maybe I made a mistake. Wait, let's think about the definition of acceleration: acceleration is the rate of change of velocity. If velocity is increasing in the rightward direction, acceleration is rightward. So the object has rightward velocity (since it's moving right) and rightward acceleration (since it's speeding up). So the correct option is e? No, option e is rightward, leftward. Wait, I must have messed up. Wait, maybe the spacing is decreasing. Wait, the diagram: the first dot, then a dot, then three close dots? No, the diagram shows: left to right, the dots are: • • • • • • • (but with increasing spacing). Wait,[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]