Question

the graph represents the relationship between velocity and time for an object moving in a straight line. which of the following statements is true? a. the object speeds up b. the object slows down c. the object moves with a constant velocity d. the object stays at rest

Explanation:

Step1: Analyze the velocity - time graph

In a velocity - time graph, if the velocity \(v\) is constant (the graph is a horizontal line), the object is moving with a constant velocity.

Step2: Check each option

• Option A: For an object to speed up, the velocity should be increasing with time (\(\frac{dv}{dt}>0\)). But the graph is horizontal (\(\frac{dv}{dt} = 0\)), so this option is wrong.
• Option B: For an object to slow down, the velocity should be decreasing with time (\(\frac{dv}{dt}<0\)). But the graph is horizontal (\(\frac{dv}{dt}=0\)), so this option is wrong.
• Option C: Since the velocity \(v\) does not change with time (\(\frac{dv}{dt} = 0\)), the object moves with a constant velocity. This option is correct.
• Option D: For an object to stay at rest, \(v = 0\). But the graph shows \(v\approx5\space m/s

eq0\), so this option is wrong.

Answer:

C. The object moves with a constant velocity