From a distance-time graph, an object moves from point A to point B, covering a distance (s₂ − s₁) in time (t₂ − t₁). Which of the following correctly represents the speed (v) of the object?

Correct option is B

The correct answer is (b) v = (s₂ − s₁) / (t₂ − t₁)

Explanation:

• Speed (v) is defined as the rate of change of distance with respect to time.

• In a distance–time graph, the speed of an object is represented by the slope of the graph.

• The change in distance (vertical axis) is:
Δs = s₂ − s₁

• The change in time (horizontal axis) is:
Δt = t₂ − t₁

• Therefore, average speed is calculated as:
v = Distance / Time = (s₂ − s₁) / (t₂ − t₁)

Information Booster:

• A straight line on a distance–time graph indicates that the object is moving with uniform speed.

• A curved line indicates non-uniform speed, meaning the object is accelerating or decelerating.

Additional Knowledge:

v = (s₁ − s₂)(t₁ − t₂) (Option a)
• This represents multiplication of differences and does not give the correct expression for speed.

v = (t₂ − t₁) / (s₂ − s₁) (Option c)
• This is the reciprocal of speed (time per distance), sometimes called pace.

v = (s₂ − s₁)(t₂ − t₁) (Option d)
• This represents the product of distance and time, which has no physical meaning in this context.