Question

which position - time graph is equivalent to the given velocity - time graph?

Explanation:

Step1: Analyze the velocity - time graph

The velocity - time graph has a negative slope (velocity is decreasing at a constant rate). The area under the velocity - time graph gives the displacement. The formula for velocity \(v = v_0+at\) (where \(a<0\) since the slope is negative), and the formula for position \(x=x_0 + v_0t+\frac{1}{2}at^{2}\). Since \(a<0\), the position - time graph is a parabola opening downwards.

Step2: Check the shape of position - time graphs

• Graphs \(A\) and \(D\) are not parabolas. Graph \(B\) is a straight - line (constant velocity, \(a = 0\)). Graph \(E\) has a positive acceleration (since the slope of the position - time graph is increasing). Graph \(F\) has a negative acceleration but the initial velocity (slope of the position - time graph at \(t = 0\)) is negative. Graph \(C\) is a parabola opening downwards with a positive initial slope (positive initial velocity) which is consistent with the velocity - time graph (positive initial velocity and negative acceleration).

Answer:

C