One hypothesis above would probably rely on the situation called <em>"inelastic collision." </em>The two carts are travelling towards each other at different speed. So, this means that once they collide, the kinetic energy will not be conserved but will be transferred as <em>sound energy, thermal energy or material deformation</em>. The impact will be great, thus a <u>greater fraction of kinetic energy will be lost from the system.</u>
The one fact that needs to be mentioned but isn't given anywhere on or around the graph is: The distance, on the vertical axis, is the distance FROM home. So any point on the graph where the distance is zero ... the point is in the x-axis ... is a point AT home.
Segment D ... Walking AWAY from home; distance increases as time increases.
Segment B ... Not walking; distance doesn't change as time increases.
Segment C ... Walking away from home, but slower than before; distance increases as time increases, but not as fast. Slope is less than segment-D.
Segment A ... Going home; distance is DEcreasing as time increases. Walking pretty fast ... the slope of the line is steep.