Question

A person runs on a 300m circular track and comes back to the starting point in 200s. Calculate the average speed and average velocity.
1. 1.5m/s, 0
2. 2.5m/s, 2 
3. 3 m/s, 3
4. 1.5m/s, 1.5m/s

Answer 1

Correct Answer - Option 1 : 1.5m/s, 0

CONCEPT:

• Average velocity: The average velocity of an object is defined as the displacement per unit of time.
• Let x₁ and x₂ be its positions at instants t₁ and t₂ respectively.
• Then mathematically we can express average velocity (v) as:

\(\Rightarrow v = \frac{displacement}{Time taken}\)

\(\Rightarrow v= \frac{x_{2} - x_{1}}{t_{2} - t_{1}}= \frac{Δ x}{Δ t}\)

where x₂ - x₁, signifies a change in position (denoted by Δx) and t₂ - t₁ is the corresponding change in time (denoted by Δt).

• Average velocity can be represented as V_av also.
• The average speed of an object is obtained by dividing the total distance travelled by the total time taken:

\(\Rightarrow Average \; speed = \frac{Total \; distance \; travelled}{total\; time \; taken}\)

• If the motion is in the same direction along a straight line, the average speed is the same as the magnitude of the average velocity. 

CALCULATION:

Given that:

The total length of the track = 300m. 

Time is taken to cover this length = 200s

\(\Rightarrow Average \; speed= \frac{Total \; distance \; travelled}{total\; time \; taken}\)

\(\Rightarrow Average \; speed= \frac{300}{200} ms^{-1} = 1.5 ms^{-1}\)

• As the person comes back to the same point, the net displacement is zero. Therefore, the average velocity is also zero.
• option 1 is the correct answer.