
Samjhiye, is section ka poora point yeh hai ki aapko Class 11 Physics ke NCERT Exemplar se kinematics ke numericals ka saamna karwana hai—sirf problems nahi, unke solutions bhi. Main focus wahi rahega jahan zyadaatar students atak jaate hain: motion in a straight line, woh teen-char equations of motion jo aapko raat ko yaad karni padti hain, relative velocity ka concept jo pehli baar mein uljha hua lagta hai, aur graphs—haan, woh slope, area, aur shape wale sawaal.
Kinematics physics ka woh hissa hai jo sirf motion ko batata hai—uske peeche ki wajah se koi matlab nahi rakhta. NCERT Class 11 ke syllabus mein yeh chapter ek dum basic cheez hai, aur iske bina aage kuch nahi banega. Chalte hain, kuch important numerical types aur unhe todne ke simple tarike dekhte hain.
Agar aap straight line uniform acceleration wale questions solve kar rahe hain, toh teen equations of motion hi aapke asli hathiyaar hain: v = u + at, s = ut + ½ at², aur v² = u² + 2as. Inko yaad rakhna hi kaafi hai. Chaliye ek simple example lete hain. Sochiye ek car bilkul rest se start hoti hai, matlab initial velocity zero. Ab woh 5 m/s² ke constant acceleration se aage badhti hai. Ab sawaal yeh hai—10 seconds baad uski velocity kya hogi aur kitna displacement cover hua? Bas in teeno mein se pehli do equations lagao, aur answer turant mil jayega.
Straight to it. You’ve got u = 0, a = 5 m/s², and t = 10 seconds. First, find the final speed. Use v = u + at. Plug in the numbers, and you get v = 0 + (5)(10), which is 50 m/s. Easy enough. Now for the distance — that’s s = ut + ½at². Since u is zero, the first term just vanishes. So you’re left with half of five times a hundred. That works out to 250 meters — clean.
Relative velocity ka funda yahan samajhna zaroori hai, kyunki do cheezein ek saath chal rahi hon to unka aapas ka motion alag hota hai. Socho ek train 20 m/s ki raftar se east ki taraf bhaag rahi hai, aur ek car bhi usi direction mein 15 m/s se chal rahi hai. Ab car ke andar baith kar dekho — train kitni tez lagti hai? Wahi relative velocity hai, aur is hisaab se 5 m/s nazar aayegi, kyunki dono same side jaa rahe hain.
Train’s hauling east at 20 m/s, car’s crawling along at 15 m/s, same lane. To get relative velocity, just subtract — 20 minus 15. Five meters per second, east. That’s it. The train’s pulling away, yeah, but only by 5 meters every single second, which feels almost lazy compared to the raw speed difference you might expect.
Velocity-time graphs and displacement-time graphs—they’re basically treasure maps for motion. The slope on a v-t graph? That’s your acceleration, plain and simple. And the area under that same curve? That hands you the total displacement. Honestly, once you get the hang of reading those two things, half the battle’s won. The Exemplar book’s packed with problems built exactly around this—practice questions that force you to dig into these graphs and pull out the answers for yourself. So yeah, don’t skip them.
Yahan acceleration fix hota hai—g, jo 9.8 m/s² hai, neeche ki taraf. Socho, ek ball ko 50 meter ki height se chhod do. Ground tak pahunchne mein kitna waqt lagega? Bas u = 0, s = 50 m, aur a = g le lo. Simple hai, seedha formula lagao.
Okay, so for this one, we just plug everything into the equation s = ut + ½ gt². The stone starts from rest, so u is zero, which wipes out that whole first term. Nice — that leaves us with 50 = ½ times 9.8 times t². You can simplify that, and you get t² is roughly 10.2. Take the square root of that, and boom—t comes out to about 3.19 seconds. That's your answer right there.
Exemplar ke questions mein aise tricky numericals aate hain jo average velocity, instantaneous velocity, aur variable acceleration ke around ghoomte hain. Inhe dekh ke lagta hai ki seedhe formulas se kaam nahi chalega—pehle basics pakke karo. Aur haan, ek baat hamesha yaad rakhna: average velocity matlab total displacement ko total time se divide karo, bas. Instantaneous velocity? Woh toh displacement ka derivative hai, time ke respect mein. Simple hai, par agar concept clear nahi hai, toh yeh problems jaan le kar aayengi.
Chapter se aane wale numericals ko agar aap roz thoda sa practice karein, toh board ho ya competitive exam, dono jagah questions seedhe aapke haath lagein ge. Koi rocket science nahi hai, bas har type ka sawal ek baar khud solve karke dekho, phir dekhna kitna aasaan lagta hai.