Part C: Concept Checks

Transcript

0:00Introduction

Hello everyone! Okay, one quick question before we start. You throw a ball straight up. At the very top, it stops for an instant, so its velocity is zero. Then at that instant, the acceleration is also zero, right? Most students say yes, without thinking. Hold your answer; in two minutes we will settle it. Today is Part C of the kinematics problem bank: quick concept checks. Assertion and reason, true or false, and graphs. And remember, in JEE, these one-line questions are where good students lose easy marks. So, let's begin.

0:38Assertion–Reason: three checks

So, let's settle our puzzle with an assertion and reason question. Now, for every such question, ask three things, in order. One: is the assertion true? Two: is the reason true? And three: does the reason explain the assertion? Okay? Here is the assertion: a body can have zero velocity and non-zero acceleration. On screen, v is the velocity, a is the acceleration, and the equals sign with a slash through it means not equal to. So, check one: is this possible? Yes, it is! Look at the reason. At the top of a vertical throw, the velocity is zero, but the acceleration is still g, the acceleration due to gravity. That is our ball, right? It stops, but its acceleration does not. So the assertion is true, and the reason is true. Now check three: does the reason explain the assertion? Yes, it does. The reason gives a real example of exactly what the assertion claims, and the example proves the assertion. So: both true, and the reason explains. And our puzzle? At the top, the velocity is zero, but the acceleration is still g, not zero. Clear now?

1:54Constant acceleration: what can it do?

Next, some true or false checks. First, a projectile in free flight, at the top of its path. True or false: there, its velocity is perpendicular to its acceleration. Yes, true! At the top, the velocity is horizontal, and the acceleration points straight down. On screen, v with an arrow on top is the velocity vector, and a with an arrow is the acceleration vector. The double arrow means so, and the upside-down T means perpendicular. Got it? Now a deeper check. Suppose a body's acceleration is constant, in magnitude and in direction. Can its velocity change direction? Can its velocity reverse? And can the body move along a circle? Change direction? Yes! Take any projectile. Its acceleration stays the same all the time, but the direction of its velocity keeps changing along the curved path. Absolutely. Reverse? Yes again: a ball thrown straight up. It goes up, stops, and comes back down, so its velocity reverses. And at that stop, velocity zero, acceleration not zero: our puzzle again! But move along a circle? No! For circular motion, the acceleration must keep turning, always towards the centre. Here the acceleration is fixed in direction, so it cannot turn. So remember: going round a circle always needs an acceleration. Keep that in mind for example two. With me?

3:24Example 1: which motion graphs are impossible

Now, example one, an easy one, on graphs. Which of these graphs are impossible? First, a speed time graph going below the axis. Second, an x t graph that is a vertical line segment. Third, an a t graph with a jump, and fourth, a v t graph with a jump. Here x is the position, v the velocity, a the acceleration, and t the time, okay? Pause the video, and try it first. Done? Okay, let's check. Below the axis would mean a negative speed. But speed cannot be negative, can it? So, impossible. Next, a vertical line on the x t graph. The slope of an x t graph is the velocity, v, and a vertical line has an infinite slope. Infinite velocity? Impossible. Now the two jumps: one on the v t graph, and one on the a t graph. Both look equally sudden. So both are impossible, right? Careful, no! Only one of them is. Look, a jump in velocity means the velocity changes in zero time, and that needs an infinite acceleration. So the jump in the v t graph is impossible. But the acceleration can jump. Switch on a force suddenly, and the acceleration changes at once. So this graph is possible, okay? This is the trap: many students cross out this graph too. So the answer: all except the a t graph with a jump. Look back at the screen: each impossible graph needed a negative speed, an infinite velocity, or an infinite acceleration. Look for these three, every time. Easy, isn't it?

5:09Example 2: assertion reason on uniform circular motion

Now a harder one, JEE level. Assertion: in uniform circular motion, the acceleration is zero, because the speed is constant. Reason: acceleration is the rate of change of speed. Uniform circular motion means moving along a circle at constant speed, okay? Use the three checks. Pause and try. Hint: speed, or velocity? Done? Okay, let's check. Assertion first. Yes, the speed is constant. But velocity is a vector, and along a circle its direction keeps changing. And a changing velocity means an acceleration: v squared by r, where v is the speed and r is the radius. Not zero! So the assertion is false. See, this is the mirror image of our puzzle. There, velocity zero, but acceleration not zero. Here, speed constant, but acceleration still not zero. Now check two, the reason: acceleration is the rate of change of speed. Sounds correct, doesn't it? So the answer is: assertion false, reason true, right? No, no, careful! This is the JEE trap. Acceleration is the rate of change of velocity, not of speed. If it were only speed, the circle would have no acceleration, and we just saw that it does. So the reason is false too. So, both false. And notice: the assertion went wrong exactly because it trusted this wrong reason. Two false statements, one wrong idea. Clear?

6:46Quick revision: zero velocity, acceleration, speed

So, quick revision. Zero velocity does not mean zero acceleration: at the top of a throw, the acceleration is still g, the acceleration due to gravity. Acceleration is the rate of change of velocity, not of speed. And in graphs, speed is never negative; velocity cannot jump, but acceleration can. Now go and try the practice problems on this page. Read every statement slowly, use the three checks, and the traps will not catch you. All the best!