Question

The slope of the tangent drawn on a position-time graph at any instant is equal to the instantaneous ____.

• A. acceleration
• B. force
• C. velocity
• D. momentum
• E. impulse

Hint:

To remember the relationships: The slope of Position-Time gives Velocity, and the slope of Velocity-Time gives Acceleration.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A position-time graph represents the variation of an object's position with respect to time.
The slope of a curve at a specific point indicates the instantaneous rate of change of the dependent variable (position) with respect to the independent variable (time).
Step 2: Key Formula or Approach:
The mathematical definition for instantaneous velocity is the first derivative of position $x$ with respect to time $t$, represented as $v = \frac{dx}{dt}$.
Step 3: Detailed Explanation:
Geometrically, the derivative $\frac{dx}{dt}$ represents the slope of the tangent line drawn to the $x-t$ curve at any particular instant.
Because the rate of change of position over time defines velocity, this slope exactly equals the object's instantaneous velocity at that moment.
Step 4: Final Answer:
The slope of the tangent drawn on a position-time graph at any instant is equal to the instantaneous velocity.