Question

An object moving along a straight line is slowing at a constant acceleration rate. Several data points are collected in the middle of the slowing process, for the object's velocity as a function of time. The data points are shown on the graph below, along with a best-fit line that has been inserted to extrapolate data for the entirety of the object's motion.
In using the graph to analyze the object's motion, several different quantities about the best fit line can be calculated.
Which quantities would be equal to the object's initial velocity, and to the object's displacement, during its slowing motion?

• A. Initial Velocity: Slope
  Displacement: Area under line
• B. Initial Velocity: x-intercept
  Displacement: Slope
• C. Initial Velocity: y-intercept
  Displacement: Area under line
• D. Initial Velocity: Slope
  Displacement: y-intercept

Answer 1

The correct option is C Initial Velocity: y-intercept

Displacement: Area under line
Initial velocity is the velocity of object at $t=0s$. Hence the y-intercept of the curve gives the initial velocity.

We know that $v=\frac{dx}{dt}$

$⟹$ Displacement$={\int }_0^{x}dx=v{\int }_0^{t}dt=$Area under the curve

Hence correct answer is option C.