the position vs time graph to the right shows the motion of an object moving along a straight path over…
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?\na) displacement is negative\nb) velocity is negative\nc) acceleration is negative\nd) none of the above - mentioned quantities are negative
Answer
Explanation:
Step1: Analyze displacement
Displacement is the final position minus the initial position. From the graph, assume initial position (x_{i}) and final position (x_{f}). If (x_{f}>x_{i}), displacement (\Delta x=x_{f} - x_{i}>0).
Step2: Analyze velocity
Velocity (v=\frac{\Delta x}{\Delta t}). The slope of the position - time graph gives velocity. If the slope is positive (graph is increasing), (v>0).
Step3: Analyze acceleration
Acceleration (a = \frac{\Delta v}{\Delta t}). The curvature of the graph (concave up) implies that the slope (velocity) is increasing. So, if (v) is increasing ((\Delta v>0)), (a=\frac{\Delta v}{\Delta t}>0) (since (\Delta t>0) for the time interval considered in the motion).
Answer:
d) none of the above - mentioned quantities are negative