Question

the position vs time graph to the right shows the motion of an object moving along a straight path over time. which of the following about the motion during the time shown in the graph is true?
a) displacement is negative
b) velocity is negative
c) acceleration is negative
d) none of the above - mentioned quantities are negative

Explanation:

Step1: Analyze displacement

Displacement is the change in position. If the final position is greater than the initial position (assuming the positive - direction is as per the coordinate system of the graph), displacement is positive. From the graph, the object moves from a lower - position region to a higher - position region (assuming the upward direction on the position - axis is positive), so displacement is positive.

Step2: Analyze velocity

Velocity \(v=\frac{\Delta x}{\Delta t}\). The slope of the position - time graph gives the velocity. The slope of the graph is positive (since the position is increasing with time), so \(v>0\).

Step3: Analyze acceleration

Acceleration \(a = \frac{\Delta v}{\Delta t}\). The slope of the velocity - time graph (derivative of the position - time graph) is negative. The slope of the position - time graph (velocity) is decreasing. If \(v = f(t)\) and \(\frac{dv}{dt}<0\), then \(a<0\).

Answer:

C. acceleration is negative