Questions: A cart slows down while moving away from the origin. What do the position and velocity graphs look like?

Transcript text: A cart slows down while moving away from the origin. What do the position and velocity graphs look like?

Solution

Solution Steps

Step 1: Understanding the Problem

We need to determine the appearance of the position and velocity graphs for a cart that is slowing down while moving away from the origin. This involves understanding the relationship between position, velocity, and acceleration.

Step 2: Analyzing Position Graph

The position graph shows how the cart's position changes over time. Since the cart is moving away from the origin, the position will increase over time. However, because the cart is slowing down, the rate of increase in position will decrease over time. This means the position graph will be a curve that starts steep and becomes less steep as time progresses.

Step 3: Analyzing Velocity Graph

The velocity graph shows how the cart's velocity changes over time. Since the cart is slowing down, its velocity is decreasing. However, because it is still moving away from the origin, the velocity remains positive but decreases towards zero. This means the velocity graph will be a downward-sloping line starting from a positive value and approaching zero.

Final Answer

The position graph will be a concave down curve, starting steep and becoming less steep over time.
The velocity graph will be a straight line with a negative slope, starting from a positive value and approaching zero.

\[ \boxed{\text{Position graph: concave down curve}} \] \[ \boxed{\text{Velocity graph: downward-sloping line}} \]

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