Overview

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Picture a truck moving along a straight road at a steady speed. From the truck, a ball is thrown straight up. Where does the ball land? Behind the truck, on the road? Or back in the truck? Hmm, don't answer too fast. Today we will solve this exact puzzle, with real numbers. And why does this matter? Kinematics gives one or two questions in almost every JEE Main shift. This chapter is where you practise them like a real test. So, let's begin.

0:37Kinematics in JEE Main

So, first, why is this chapter so important? Kinematics gives one or two questions in almost every JEE Main shift. Almost every shift, okay? These are marks you simply cannot leave. Now tell me. These one or two questions: which topics of kinematics do they come from? From the whole unit, that's right! Averages, the equations of motion, and motion under gravity. Then graphs, projectiles, relative motion and circular motion. Any one of them can come in your paper. Clear? And where are the real past questions? The real JEE Main questions, from twenty twenty one to twenty twenty six, are at the end of Chapters one to six. The problems in this chapter are original, but written in exactly the same style.

1:29Three sets, 15 problems in each

Now, what is inside this chapter? Three sets of mixed problems, with fifteen original problems in each set, okay? Set one: the straight line, and graphs. Set two: vectors and projectiles. With me? And set three: relative motion and circular motion. And remember our truck puzzle from the start? It lives right here, in set three. So the whole unit is mixed together, and for every problem, you first have to spot the idea yourself.

1:59Treat each set as a test

Now, the most important instruction of this chapter. Each problem should take you just one to two minutes, okay? So tell me. Fifteen problems, one to two minutes each. How long should one whole set take? Fifteen to thirty minutes, exactly! The double arrow on screen simply means "so", okay? So sit with a clock, and treat every set like a small test. Alright, now the trap. You are on problem five, you feel a little stuck, and the solution is right there on the page. Just one small look, what is the harm, right? No, no, careful! Reading a solution and nodding is not the same as solving the problem. So the rule is: attempt the whole set before reading any solution. Your own answers on paper first, right or wrong. Then compare, and learn from every mistake. Got it?

2:52Topper's trick: g=10 keeps the maths quick

Now one rule that runs through every problem here. Take g equal to ten, unless the question tells you otherwise. Here g is the acceleration due to gravity, and m s to the power minus two means metres per second squared, okay? Now, for a body falling from rest, the height fallen is half g t squared, where t is the time. With g equal to ten, what does half g t squared become? Five t squared, exactly right! Half of ten is five, so h, the height fallen, equals five t squared. Nice and quick. So a stone that falls from rest for three seconds falls five into three squared. Three squared is nine, so five into nine: forty five metres. The cross on screen means into, okay? No calculator, all in your head. That is the speed these problems want.

3:42Example 1: second-half speed to average 48 km/h

Now, let's practise exactly the way this chapter says. This one is from Set one, and it is an easy one. Here, a car covers the first half of a distance at forty kilometres per hour. On screen, k m h to the power minus one means kilometres per hour, okay? At what speed must it cover the second half, to average forty eight kilometres per hour? Pause the video and try it. Your two minutes start now. Done? Okay, let's check. Call the second speed v. Most students write: forty plus v, divided by two, equals forty eight. So v is fifty six, right? No, no, careful! That is the JEE trap. The simple average works only for equal times, not for equal distances. For two equal distances, the average speed, v with a small a v g below it, equals two v one v two, by v one plus v two. Here the small one and two below v mark the two speeds, okay? So, two into forty into v, by forty plus v, equals forty eight. The dot means into. Clear? Cross multiply. Eighty v equals one thousand nine hundred and twenty, plus forty eight v. So thirty two v equals one thousand nine hundred and twenty, and v is sixty kilometres per hour. That's it! And a quick check, the way toppers do it. Two into forty into sixty is four thousand eight hundred, and forty plus sixty is one hundred. Four thousand eight hundred by one hundred: forty eight. Perfect match!

5:14Example 2: ball thrown up from a moving truck

Now a harder one, from Set three, and it is our puzzle from the start! Here, a ball is thrown vertically up at twenty metres per second, relative to a truck. On screen, m s to the power minus one means metres per second, okay? The truck moves at a steady ten metres per second. Describe the path of the ball as seen from the ground, and find where it lands, from the launch point on the road. Pause and try. Hint: look at it from the ground. Done? Okay, let's check. Most students say: the ball goes straight up and comes straight down. Meanwhile the truck moves ahead, so the ball falls behind the truck, right? No, no, careful! Before the throw, the ball was already moving with the truck, at ten metres per second, remember? So from the ground, its velocity has two components: u x, ten forward, and u y, twenty upward. The small x and y below u mean the horizontal and vertical parts, okay? Forward motion, upward motion, and gravity pulling down. So from the ground, it is just a projectile, and its path is a parabola. Got it? Now the time in the air, capital T, equals two u y by g. Two into twenty, by ten: four seconds. In these four seconds, the ball's distance along the road, x, is u x into T: ten into four, forty metres. Now the real question of our puzzle. Where is the truck after these same four seconds? The truck also moves ten into four, forty metres, exactly! Ball, forty metres. Truck, forty metres. So the ball lands back in the truck! Puzzle solved. You see, the ball does land forty metres further along the road, but the truck has moved forward with it. Relative motion and projectiles in one question: that is what a mixed problem looks like.

7:11Quick revision: time per problem, g = 10, try first

So, quick revision. Kinematics gives one or two questions in almost every JEE Main shift. Each problem should take one to two minutes, and take g equal to ten, unless told otherwise. And attempt the whole set before reading any solution. Now open Set one, start your clock, and begin. You can do this, I promise. All the best!