Question

study the image of the roller coaster, then answer the questions. note that the arrows indicate the direction of the movement of the roller coaster train. which section (a or b) of the roller coaster shows positive acceleration? which section (a or b) of the roller coaster shows negative acceleration?

Explanation:

First Sub - Question (Positive Acceleration)

Step1: Recall Acceleration Definition

Acceleration is positive when velocity and acceleration are in the same direction. For a roller - coaster, when it's moving upwards (increasing speed in the upward direction) or downwards but speeding up in the downward direction? Wait, no. Let's think about the direction of motion. In section B, the roller - coaster is moving upwards (the arrow is upward). If it's moving upwards and speeding up (or if the direction of acceleration is the same as the direction of velocity), then acceleration is positive. In section A, the roller - coaster is moving downwards. If it's moving downwards and slowing down, that would be negative acceleration, but if it's moving downwards and speeding up? Wait, no. Wait, positive acceleration is when the acceleration vector is in the same direction as the velocity vector. So in section B, the velocity is upward. If the roller - coaster is moving upward and its speed is increasing (for example, coming out of a low point and moving up, maybe after a drop, but in this case, the arrow for B is upward. So if the roller - coaster is accelerating in the direction of motion (upward), then B has positive acceleration. In section A, the motion is downward. If the roller - coaster is slowing down while moving downward (like approaching the bottom of a drop and then moving up? No, A's arrow is downward. Wait, maybe A is moving downward but slowing down (so acceleration is upward, opposite to velocity, negative acceleration), and B is moving upward and speeding up (acceleration same as velocity, positive acceleration). So for positive acceleration, the section where velocity and acceleration are in the same direction. So B: velocity is upward, acceleration (if it's speeding up) is upward, so positive acceleration.

Step2: Determine Positive Acceleration Section

So section B shows positive acceleration because the direction of motion (velocity) and the direction of acceleration (if it's speeding up in that direction) are the same.

Second Sub - Question (Negative Acceleration)

Step1: Recall Negative Acceleration Definition

Negative acceleration (deceleration) occurs when the acceleration vector is opposite to the velocity vector. In section A, the roller - coaster is moving downward (velocity direction is downward). If it is slowing down while moving downward (for example, approaching the bottom of the track and starting to change direction or just slowing down), then the acceleration is upward (opposite to velocity), so negative acceleration. In section B, as we thought before, velocity and acceleration are in the same direction (positive acceleration). So section A has negative acceleration because the acceleration is opposite to the direction of motion (velocity is downward, acceleration is upward).

Step2: Determine Negative Acceleration Section

So section A shows negative acceleration.

Answer:

For positive acceleration: B
For negative acceleration: A