Vardaan Institute - Physics Master Worksheet

Section A: Differentiation & Rates of Change

Differentiate $y = 3x^4 - 5x^2 + 7x - 9$ with respect to $x$.

If position of a particle is $x(t) = 2t^3 - 9t^2 + 12t + 5$, find the velocity at $t = 2\text{ s}$ and acceleration when velocity is zero.

Evaluate $\frac{d}{dx} \left( \frac{\sin x}{x} \right)$ using quotient rule.

Section B: Integration & Definite Integrals

Evaluate the indefinite integral $\int (4x^3 - 6x^2 + 2x - 5) \, dx$.

Calculate the work done $W = \int_{1}^{3} (3x^2 + 2x) \, dx$.

Section C: Trigonometry & Maxima/Minima

Find the maximum and minimum values of $y = 3\sin x + 4\cos x$.

Find the critical points of $f(x) = x^3 - 3x + 2$ and determine where it achieves relative maxima and minima.

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