PhysicsClassical Physics

How to Calculate Displacement: Tiana’s Three-Segment Jog

Signed one-dimensional position changes give a net displacement of −0.2 km, while adding all three path segments gives a total distance of 4.6 km.

Question

Tiana jogs 1.5 km in one direction along a straight path, then 2.4 km in the opposite direction, then 0.7 km back in her original direction. Take the original direction as positive.1. What is her net displacement?2. What total distance did she jog?

Answer

Use signs for displacement because direction matters. With the original direction positive,

Δx=(+1.5km)+(2.4km)+(+0.7km)=0.2km.\Delta x=(+1.5\,\text{km})+(-2.4\,\text{km})+(+0.7\,\text{km})=-0.2\,\text{km}.

So Tiana’s displacement is −0.2 km, meaning she finishes 0.2 km in the direction opposite to where she first started jogging.

For distance, add the lengths of all three path segments without signs:

d=1.5+2.4+0.7=4.6km.d=1.5+2.4+0.7=4.6\,\text{km}.

Therefore:

  • Displacement: 0.2km-0.2\,\text{km}
  • Distance: 4.6km4.6\,\text{km}

The two values differ because displacement depends only on the starting and ending positions, while distance counts the entire path traveled.

Evidence boundary

This solution treats the motion as one-dimensional and uses the problem’s stated convention that Tiana’s original direction is positive. It distinguishes signed displacement from total path length; it does not infer any unstated turns, detours, or two-dimensional motion.

Sources

These references support the concepts and methods used in the explanation above.

How to Calculate Displacement: Three-Segment Jog | Verla