Q.11 NEET 2026 Important Model Based on Basic Mathematical Tools :Kinematics скачать в хорошем качестве

Q.11 NEET 2026 Important Model Based on Basic Mathematical Tools :Kinematics

A particle moves from Point B to C with the velocity equation:$$V = 3t^2 + 2t + t + 6$$Find the displacement covered and the acceleration of the particle at $t = 2s$.1. Simplification of Velocity EquationFirst, combine the like terms in the given expression:$V = 3t^2 + (2t + t) + 6$$V = 3t^2 + 3t + 6$2. Finding Acceleration (Differentiation)Acceleration ($a$) is the instantaneous rate of change of velocity. We find this by taking the first derivative of the velocity function with respect to time ($t$).Calculus Rule Used: The Power RuleFor any term $at^n$, the derivative is: $\frac{d}{dt}(at^n) = n \cdot at^{n-1}$Derivative of $3t^2$: $2 \times 3t^{(2-1)} = 6t$Derivative of $3t$: $1 \times 3t^{(1-1)} = 3$Derivative of constant $6$: $0$Acceleration Equation:$$a = \frac{dV}{dt} = 6t + 3$$Calculation at $t = 2s$:$a = 6(2) + 3$$a = 12 + 3 = \mathbf{15 \, ms^{-2}}$3. Finding Displacement (Integration)Displacement ($s$) is the integral of velocity over time. It represents the total "area under the curve" of a velocity-time graph.Calculus Rule Used: Integration Power RuleThe integral of $t^n$ is: $\int t^n \, dt = \frac{t^{n+1}}{n+1}$Integral of $3t^2$: $3 \cdot \frac{t^3}{3} = t^3$Integral of $3t$: $3 \cdot \frac{t^2}{2} = 1.5t^2$Integral of $6$: $6t$Displacement Equation:$$s = \int (3t^2 + 3t + 6) \, dt = t^3 + 1.5t^2 + 6t$$Calculation from $t = 0$ to $t = 2s$:$s = (2)^3 + 1.5(2)^2 + 6(2)$$s = 8 + (1.5 \times 4) + 12$$s = 8 + 6 + 12 = \mathbf{26 \, m}$Final ResultDisplacement: $26 \, m$Acceleration: $15 \, ms^{-2}$Correct Option: 1)#NEETPhysics #RotationalMotion #PhysicsTricks #NEET2026 #PhysicsConcepts #AngularMomentum #MedicalEntrance #JEE #jeeaprilattempt #jeejanuaryattempt #jeeadvanced #mhtcetlatestupdates #kcet #rotationalmotion #education #physicstricks #SHORTCUTSINPHYSICS #physics #ncertsolutions #ncertphysics #neetncert#2025 Rank Saver #📉: Don't let tough Physics kill your rank again. •#2. @600# Elite Questions 🎯: Master 600 models; cover 100% concepts. •3. @#Target 150+ Marks 🏆: Lock in your score with surgical precision. •4. @#2-Hour Daily Limit ⏳: Max results in minimum time—save energy for Bio. •5. @#40-Day Masterplan 🗓️: 15 numericals a day to finish the entire syllabus. •6. @#Concept Clarity 💡: We teach the "Why," not just the solution. •7. @#Live Doubt Marathons 🏃‍♂️: Weekly live sessions to clear every hurdle. •8. @#5 Full PCB Mock Tests 📝: Realistic 720-mark practice for exam grit. •9. @#Darna Mana Hai 🛡️: Zero stress. One platform. Total confidence. 10. @#Just ₹2500 💎: Premium coaching at the best price. Watch demos now!