Position Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Position.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The location of an object relative to a chosen reference point (origin), described using coordinates in a given reference frame.

Where something is, described by numbers from some starting point.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Position starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to position but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?

Worked Examples

Example 1

easy
An object starts at position x=3 mx = 3 \text{ m} and moves to x=11 mx = 11 \text{ m} along a straight line. What is the object's displacement?

Answer

Δx=8 m\Delta x = 8 \text{ m}

First step

1
Position is a specific location on a coordinate axis. The initial position is xi=3 mx_i = 3 \text{ m} and the final position is xf=11 mx_f = 11 \text{ m}.

Full solution

  1. 2
    Displacement is the change in position: Δx=xf−xi=11−3=8 m\Delta x = x_f - x_i = 11 - 3 = 8 \text{ m}
  2. 3
    The displacement is 8 m8 \text{ m} in the positive direction.
Position describes where an object is located relative to a chosen origin. Displacement is the change in position and is independent of the path taken between the two positions.

Example 2

medium
A particle's position is given by x(t)=4t2−2t+1x(t) = 4t^2 - 2t + 1 (in meters, with tt in seconds). What is the particle's position at t=0 st = 0 \text{ s} and t=3 st = 3 \text{ s}? What is the displacement between these times?

Example 3

medium
A bug's position is x(t)=2t+1x(t) = 2t + 1 (meters, tt in seconds). What is its position at t=4 st = 4 \text{ s}?

Example 4

medium
A car's position is x(t)=5t2x(t) = 5t^2 meters. Find its position at t=2 st = 2 \text{ s} and t=5 st = 5 \text{ s}, then the displacement between these times.

Example 5

medium
A ball's position is y(t)=20−5t2y(t) = 20 - 5t^2 meters (up positive, ground at y=0y=0). At what time does it hit the ground?

Example 6

hard
A particle's position is x(t)=t2−6t+5x(t) = t^2 - 6t + 5 (meters). At what times is the particle at x=0x = 0?

Example 7

hard
A ball's position is y(t)=1.5+10t−5t2y(t) = 1.5 + 10t - 5t^2 meters (up positive). Find the time of maximum height and the maximum height above the ground.

Example 8

challenge
A train sits at position xT=+120 mx_T = +120 \text{ m} in the platform frame. The platform frame moves at +5 m/s+5 \text{ m/s} relative to a car frame; at t=0t=0 the two frames' origins coincide. What is the train's position in the car frame at t=4 st = 4 \text{ s} (treat the train as instantaneously at rest in the platform frame)?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
An ant walks from position x=−5 mx = -5 \text{ m} to x=7 mx = 7 \text{ m}, then back to x=2 mx = 2 \text{ m}. What is the total distance traveled and the final displacement from the starting point?

Example 2

hard
A particle's position is x(t)=t3−6t2+9tx(t) = t^3 - 6t^2 + 9t (meters). At what times is the particle at position x=0x = 0? What is the velocity at each of those times?

Example 3

easy
A point is at x=5x = 5 m on a number line whose origin is the front door. What is its position?

Example 4

easy
An ant sits 3 m left of the origin. Taking right as positive, what is its position?

Example 5

easy
A car is at the 2020 km marker on a highway measured from town. State its position relative to town.

Example 6

easy
Object A is at x=2x=2 m and object B is at x=9x=9 m. Which has the larger coordinate?

Example 7

easy
A runner starts at the origin. Where is the origin's position coordinate?

Example 8

easy
Taking up as positive, a drone hovers 1212 m above the ground origin. Its position?

Example 9

easy
A bead is at x=−4x=-4 cm. Is it left or right of the origin if right is positive?

Example 10

easy
Two flags are placed at x=10x=10 m and x=10x=10 m in the same frame. Are they at the same position?

Example 11

medium
A cyclist's position is x=3x=3 m at the start and x=11x=11 m later, same frame. By inspection, on which side of the start is she now and how far along the axis?

Example 12

medium
A train's position relative to the platform is xp=+50x_p=+50 m, but relative to a moving car the same train is at xc=−20x_c=-20 m. Why do they differ?

Example 13

medium
On an xx-axis (right positive), point P is 77 m right of origin and point Q is 55 m left. Give both positions and which is greater.

Example 14

medium
A snail is at x=2x=2 m. The origin is shifted 22 m to the right (new origin where the snail was). What is the snail's new position coordinate?

Example 15

medium
A hiker's positions at three times are x=0, 4, 1x=0,\ 4,\ 1 m. Which is the maximum position and which the minimum?

Example 16

medium
A ball on a vertical axis (up positive) is at y=+6y=+6 m then later at y=−2y=-2 m. Has it ended above or below the origin?

Example 17

challenge
A car's position is x=120x=120 m from town A and x=80x=80 m from town B (towns are on a line, A left of B). If A is the origin, what is B's position coordinate?

Example 18

challenge
Positions of a particle (in m) follow x(t)=t2−4tx(t)=t^2-4t for tt in seconds. At what time is the particle back at the origin (other than t=0t=0)?

Example 19

challenge
A point moves so its position is x=−3x=-3 m, then origin is redefined at x=−3x=-3 m AND positive direction is reversed. What is the point's new coordinate?

Example 20

medium
Three checkpoints are at x=2, 7, 15x=2,\ 7,\ 15 m. A scout claims the middle checkpoint is exactly halfway between the outer two. Is the claim true?

Example 21

medium
On a number line (right positive), a car moves so its position goes −6-6 m, 00 m, +4+4 m at three times. State which reading is farthest from the origin.

Example 22

medium
A marker is at x=15x=15 m from gate A. Gate B is 99 m right of gate A. What is the marker's position measured from gate B?

Example 23

easy
A book sits on a shelf 1.4 m1.4 \text{ m} above the floor. Taking the floor as the origin and up as positive, what is the book's position?

Example 24

easy
Two pens lie on a desk. Pen A is at x=12 cmx = 12 \text{ cm} and pen B is at x=5 cmx = 5 \text{ cm} from the desk's left edge. Which pen is farther from the origin?

Example 25

easy
A swimmer is at x=−8 mx = -8 \text{ m} and a buoy is at x=−3 mx = -3 \text{ m} on the same axis (right positive). Which has the LARGER coordinate?

Example 26

easy
A rock sits on the bottom of a pond, 2.5 m2.5 \text{ m} below the water surface. Taking the surface as origin and up as positive, what is the rock's position?

Example 27

medium
A particle moves with x(t)=10−3tx(t) = 10 - 3t (meters). At what time does it cross the origin?

Example 28

medium
On a 2D map taking east-xx and north-yy positive, a hiker is 300 m300 \text{ m} east and 400 m400 \text{ m} north of camp. Give her position as a coordinate pair, and her straight-line distance from camp.

Example 29

medium
A mouse is at x=0.40 mx = 0.40 \text{ m} relative to the corner of a desk. If the origin is moved 0.15 m0.15 \text{ m} to the right, what is the mouse's new position coordinate?

Example 30

medium
A delivery truck is at mile marker 4242 on a highway. Its depot is at mile marker 3030. Taking the depot as origin and increasing markers as positive, what is the truck's position?

Example 31

medium
A skateboarder's positions at t=0,1,2,3 st = 0, 1, 2, 3 \text{ s} are 0,3,8,15 m0, 3, 8, 15 \text{ m}. Is the motion uniform (constant velocity)?

Example 32

medium
Town A is the origin. Town B is 40 km40 \text{ km} east of A. A truck is 25 km25 \text{ km} east of B. Find the truck's position in A's frame.

Example 33

medium
A scientist tracks the position of a particle at three times: x1=+4x_1 = +4, x2=−2x_2 = -2, x3=+1x_3 = +1 meters. What is the largest absolute displacement between any pair of these readings?

Example 34

medium
A ladybug starts at x=8 cmx = 8 \text{ cm} and walks until it reaches x=−2 cmx = -2 \text{ cm}. Find the displacement.

Example 35

hard
Two cars share an xx-axis. Car A's position is xA(t)=5tx_A(t) = 5t, car B's is xB(t)=30−5tx_B(t) = 30 - 5t (meters). At what time and position do they meet?

Example 36

hard
A particle has x(t)=3t2−12t+7x(t) = 3t^2 - 12t + 7 meters. Find the time and value of its minimum position.

Example 37

challenge
A particle's position is x(t)=t3−9tx(t) = t^3 - 9t meters. At what times is the particle exactly 4 m4 \text{ m} from the origin?
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Related Concepts

DisplacementVelocity