Question

15 which graph best represents a positive acceleration? a velocity (m/s) vs time (s) (horizontal line) b distance (m) vs time (s) (straight line) c distance (m) vs time (s) (curve then flat) d velocity (m/s) vs time (s) (increasing line)

Explanation:

To determine which graph represents positive acceleration, we analyze each option:

• Option A: The velocity - time graph is horizontal. This means velocity ($v$) is constant over time ($t$). Acceleration ($a$) is defined as the rate of change of velocity, $a=\frac{\Delta v}{\Delta t}$. If $\Delta v = 0$, then $a = 0$, so this is not positive acceleration.
• Option B: This is a distance - time graph with a constant slope. The slope of a distance - time graph represents velocity ($v=\frac{\Delta d}{\Delta t}$). A constant slope means constant velocity, and again, acceleration (rate of change of velocity) is zero.
• Option C: This is a distance - time graph. The slope (velocity) first increases (which would imply positive acceleration) and then becomes constant (zero acceleration) and then maybe zero (if it's a flat line at the end). But the question is about a graph that best represents positive acceleration. The key here is that for a graph to represent positive acceleration, we can look at velocity - time graphs (since acceleration is the derivative of velocity with respect to time) or analyze the change in velocity from distance - time graphs. However, the shape here is more complex and not the most straightforward representation of positive acceleration.
• Option D: This is a velocity - time graph. The slope of a velocity - time graph is equal to acceleration ($a=\frac{\Delta v}{\Delta t}$). The graph has a positive slope (going up from left to right), which means that velocity is increasing over time. Since acceleration is the rate of change of velocity, a positive slope in a velocity - time graph indicates positive acceleration.

Answer:

D. The velocity - time graph with a positive slope (increasing velocity over time)