On a velocity-time graph for a particle,suppose the plot starts at some positive velocity and then follows a straight line to zero at a later time.Which of the following must be true about a position vs.time graph for this same time interval?
A)The curve will start at a positive position value and follow a straight line to zero at the later time.
B)The curve will rise steeply at first and as time goes on will level out approaching its highest position value at the later time.
C)The curve will drop steeply at first and as time goes on will approach its lowest position value at the later time
D)The curve will start at the zero of position and follow a straight line to its highest position at the later time.

Question

Quizplus · Accepted Answer

Since the velocity is decreasing uniformly with time, it indicates that the particle is slowing down at a constant rate. This means that the particle is decelerating, and thus the acceleration is negative. Using the kinematic equations, we know that for a particle with constant negative acceleration, the position-time graph is a downward-facing parabola. Therefore, the curve will rise steeply at first (due to positive initial velocity) and as time goes on will level out approaching its highest position value (at the vertex of the parabola) at the later time.

On a Velocity-Time Graph for a Particle,suppose the Plot Starts