Question

2 an object starts from rest and undergoes a positive velocity change for ten seconds. it then continues on with constant positive velocity. which of the following graphs correctly describes this situation? graph a graph b graph c graph d graph e

Explanation:

Step1: Analyze the motion during the first 10 seconds

When the object starts from rest and has a positive velocity change (accelerating), the position - time graph has a curve. The slope of the position - time graph represents velocity. Since the velocity is increasing (positive acceleration), the slope of the position - time graph is increasing. The general formula for the position of an object with constant acceleration \(a\) starting from rest (\(u = 0\)) is \(x=\frac{1}{2}at^{2}\), which is a parabola opening upwards.

Step2: Analyze the motion after 10 seconds

When the object has a constant positive velocity, the slope of the position - time graph is constant. A constant slope means the graph is a straight line.

Now let's check each graph:

• Graph A: The first part has an increasing slope (accelerating) and the second part has a constant slope (constant velocity).
• Graph B: The first part has a constant slope (constant velocity from \(t = 0\), but the object starts from rest and accelerates, so this is wrong).
• Graph C: The slope is decreasing (negative acceleration or deceleration in the first part, which is not the case here).
• Graph D: The slope becomes zero (object stops moving) after some time, but the object has a constant positive velocity (non - zero slope) after \(t = 10\) s.
• Graph E: The slope is increasing throughout (object is always accelerating, no constant velocity part)

Answer:

A. Graph A