Category: HC Verma Part 1: Mechanics

Problem Statement Solve the kinematics problem: The position of a particle is given by $x = 5t^2 + 3t + 2$ (SI). Find its velocity at $t = 2$ s. $v = dx/dt$ (slope of $x$-$t$ graph) Step 1: $v = \dfrac{dx}{dt} = 10t + 3$. Step 2: At $t = 2$: $v = 10(2)…

Problem Statement Explain what the area under an $x$-$t$ (position-time) graph represents physically. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to…

Problem Statement Solve the kinematics problem: A particle starts from rest and accelerates uniformly to 20 m/s in 4 s. Find the displacement using the $v$-$t$ graph. Displacement = area under $v$-$t$ graph Step 1: The $v$-$t$ graph is a straight line from $(0,0)$ to $(4, 20)$ — a triangle. Step 2: Area = $\dfrac{1}{2}…

Problem Statement Find the maximum value of $y = 6x – x^2$ and the value of $x$ at which it occurs. Given Information $y = 6x$ Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically…

Problem Statement Solve the kinematics problem: A particle has velocity $v = u + at$. Starting from $x = 0$ at $t = 0$, find the displacement at time $t$. $x = \int_0^t v\, dt$ Step 1: $x = \displaystyle\int_0^t (u + at’)\,dt’ = \left[ut’ + \frac{a t’^2}{2}\right]_0^t$. Step 2: $x = ut + \dfrac{1}{2}at^2$.…

Problem Statement If $x = A\sin(\omega t)$, find $dx/dt$ and $d^2x/dt^2$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to units and…

Problem Statement Find $\vec{A}\times\vec{B}$ if $\vec{A} = 2\hat{i}+3\hat{j}$ and $\vec{B} = \hat{i}+2\hat{j}$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention to units…

Problem Statement Find the angle between $\vec{A} = \hat{i} + \hat{j}$ and $\vec{B} = \hat{i} – \hat{j}$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically…

Problem Statement Three vectors are $\vec{A} = 2\hat{i}$, $\vec{B} = 3\hat{j}$, $\vec{C} = 4\hat{k}$. Find $|\vec{A}+\vec{B}+\vec{C}|$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with…

Problem Statement Find the unit vector along $\vec{A} + \vec{B}$ if $\vec{A} = 2\hat{i} + 3\hat{j}$ and $\vec{B} = \hat{i} – \hat{j}$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations…