Category: HC Verma Part 1: Mechanics

Problem Statement Solve the kinematics problem: A particle moves in a circle of radius 0.5 m at constant speed 2 m/s. Find the centripetal acceleration. Centripetal acceleration $a_c = v^2/r$ Step 1: $a_c = v^2/r = 4/0.5 = 8$ m/s². $$\boxed{a_c = 8\text{ m/s}^2}$$ Given Information $a_c = v^2/r = 4/$ $\boxed{a_c = 8\text{ m/s}$…

Problem Statement Solve the kinematics problem: A ball is thrown horizontally at 10 m/s from a point 45 m above the ground on a vertical cliff. Find the horizontal range. ($g = 10$ m/s²) $t = \sqrt{2h/g}$; Range $= v_x \times t$ Step 1: $t = \sqrt{2(45)/10} = \sqrt{9} = 3$ s. Step 2: Range…

Problem Statement Solve the kinematics problem: A projectile is fired at 50 m/s at 37° to the horizontal. What is the velocity at the highest point? ($\sin 37° = 0.6$, $\cos 37° = 0.8$) At the highest point, vertical velocity = 0; only horizontal component remains. Step 1: Horizontal component (constant throughout): $v_x = 50\cos…

Problem Statement Body A starts from rest at the origin with acceleration 3 m/s². Body B starts at $x = 40$ m at the same instant and moves towards the origin at constant 5 m/s. Find when and where they meet. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement Solve the kinematics problem: A particle has acceleration $a = (4t – 2)$ m/s². At $t = 0$, $v = 3$ m/s. Find the velocity at $t = 3$ s. $v = v_0 + \int_0^t a\,dt$ Step 1: $v = 3 + \displaystyle\int_0^3 (4t-2)\,dt = 3 + \left[2t^2 – 2t\right]_0^3$. Step 2: $=…

Problem Statement A particle’s velocity is $v = (2t + 3)$ m/s. If $x = 0$ at $t = 0$, find position at $t = 2$ s. 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…

Problem Statement An elevator moves up at 5 m/s. A stone is dropped from it when it is 50 m above the ground. How long does the stone take to reach the ground? ($g = 10$ m/s²) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics…

Problem Statement Ball A is thrown upward at 20 m/s; simultaneously ball B is dropped from a height of 60 m. Find when and where they meet. ($g = 10$ m/s²) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement Solve the kinematics problem: A particle’s velocity changes from 5 m/s to 25 m/s in 4 s. Find the acceleration assuming it is uniform. $a = \Delta v / \Delta t$ Step 1: $a = (25 – 5)/4 = 20/4 = 5$ m/s². $$\boxed{a = 5\text{ m/s}^2}$$ Given Information $a = (25 –…

Problem Statement A swimmer swims at 3 m/s in still water; river flows at 4 m/s. At what angle upstream should she swim to minimize drift? What is the minimum drift? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…