Final answer:
A distance versus time graph can represent an object's motion, exhibiting a curved line for an object with constant acceleration. A displacement versus time squared graph will display a straight line under constant acceleration. Unlike position vs time for speeding up, a velocity vs time graph with constant acceleration will be a straight line.
Step-by-step explanation:
The motion of an object can indeed be shown on a line graph by plotting distance versus time. This is a standard approach to analyzing the kinematics of an object in motion. When plotting displacement versus time for an object with constant acceleration, the resulting graph will be curved, indicating that displacement is changing at a changing rate over time. However, if we plot displacement versus the square of time, this graph will indeed be a straight line for an object with constant acceleration. This directly reflects the kinematic equation for constant acceleration (s = ut + 0.5at2).
The position vs time graph of an object that is speeding up will not be a straight line; this graph will be curved to show the increasing velocity over time. On the other hand, the velocity vs time graph will provide a straight line if the object's acceleration is constant, as the slope of this line represents the acceleration. Therefore, for given acceleration, graphical analysis of an object's motion graph can be very informative about the object's kinematics, including aspects such as speed, velocity, acceleration, and displacement.