Question

Velocity of particle varies with position as shown in figure. Find the correct variation of acceleration with position. 

• A. A
• B. B
• C. C
• D. D

Hint:

When velocity is given as function of position, use $a = v \dfrac{dv}{dx}$.

Answer 1

The Correct Option is D

Step 1: Express velocity as function of position.
From graph, velocity decreases linearly with position:
\[ v = -mx + c \]
Step 2: Relation between acceleration and velocity.
\[ a = v \dfrac{dv}{dx} \]
Step 3: Differentiating velocity.
\[ \dfrac{dv}{dx} = -m \]
Step 4: Expression for acceleration.
\[ a = (-mx + c)(-m) = m^2 x - mc \]
Thus, acceleration varies linearly with position with positive slope.