Practice equation to calculate displacement & distance for one dimensional motion of the particle under constant & average acceleration. Learn formula for average speed & velocity problems equation.

- Displacement is defined as the change in the position vector of a particle. It is independent of path covered.
- Change in the position vector = Displacement
- Here in this diagram, Displacement \(=100-0\) \(=100\,m\)

- Distance is defined as the total path covered by a particle during the journey.
- So, total path covered by the particle as shown in figure \(=300+200=500\,m\)

A \(40\,m,\;80\,m\)

B \(-40\,m,\;80\,m\)

C \(-40\,m,\;-80\,m\)

D \(-20\,m,\;-70\,m\)

Average velocity is defined as the ratio of total displacement to the total time taken by moving particle.

\(\text{Average velocity}=\dfrac{\Delta x}{\Delta t}\) \(\big[\Delta x=\text{displacement},\;\Delta t=\text{total time taken}\big]\)

Average speed is defined as the ratio of total path length to the total time taken by the moving particle to cover the distance.

\(\text{Average speed}=\dfrac{s}{\Delta t}\)

**Note :** Displacement and average velocity can either be positive or negative, whereas, both distance and speed, will always be positive.

\(\implies\;s\geq\Delta x\)

\(or, \,\;\text{Average speed}\geq\text{Average velocity}\)

- For one dimensional motion :

(i) If particle does not change its direction, then

Magnitude of average speed = Magnitude of average velocity

(ii) If particle changes its direction, then

Magnitude of average speed > Magnitude of average velocity

A Average speed

B Average velocity

C Same

D Can not be determined

A \(70\,m/sec\)

B \(100\,m/sec\)

C \(90\,m/sec\)

D \(75\,m/sec\)

- If direction of the velocity does not change for one dimensional motion, then

Distance = Displacement

- If direction of the velocity changes, then initial velocity and acceleration will be in opposite direction.
- To calculate distance in this situation, follow the given steps :

**Step-1 : **Find magnitude of displacement before the velocity becomes zero i.e., \(|\Delta x_1|\)

**Step-2 :** Find magnitude of displacement after the velocity becomes zero i.e., \(|\Delta x_2|\)

**Step-3 : ** \(|\Delta x|=|\Delta x_1|+|\Delta x_2|\)

\(\therefore\;s=|\Delta x|\)

A \(32.5\,m\)

B \(62.5\,m\)

C \(70.6\,m\)

D \(80\,m\)

A 52 m/sec

B 43.33 m/sec

C 50 m/sec

D 80.67 m/sec

- If initial velocity = 0 and acceleration of particle is constant and particle does not change its direction then,

Magnitude of Displacement = Magnitude of Distance