Question

The position-time relation of a particle moving along the x-axis is given by $x=a-bt+ct^2$. The velocity-time graph of the particle is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Derivative of a quadratic position function always results in a linear velocity function.

Answer 1

The Correct Option is C

Step 1: Concept
Velocity $v$ is the first derivative of position $x$ with respect to time $t$.
Step 2: Analysis
Given $x = a - bt + ct^2$.
$v = \frac{dx}{dt} = \frac{d}{dt}(a - bt + ct^2) = -b + 2ct$.
Step 3: Conclusion
The equation $v = 2ct - b$ is in the form $y = mx + c$, which represents a straight line with a positive slope ($2c$). Final Answer:(C)