Answer
b is acceleration, a is jerk ,and graph d is position, c is velocity.
Work Step by Step
c and d are velocity and position .
Graph d is always increasing, thus the slope is always positive. Graph c always positive, which corresponds to what the derivative of d must look like. Velocity is the derivative of position.
Graph b is acceleration.
Acceleration is velocity equivalent. We know the velocity always decreases as the acceleration increases. As the acceleration reaches its peak, the velocity continues to climb at a slower rate. After the acceleration gets negative, the speed starts to decrease. When graph b descends below the x-axis, graph c starts to decline.
Graph a is the jerk.
Jerk is the derivative of acceleration. The slope of the acceleration increases up until its maximum point, the jerk is positive. Once the acceleration begins to decrease, its slope is negative, thus is graph a, or the jerk.
