 Let's solve a question on direction of acceleration and velocity now here We have at t equals to zero the velocity and acceleration of a particle is v That is plus five meters per second and a that is plus one meters per second square From t equals to zero to t equals to t naught the acceleration Decreases from one to zero point five meters per second square and the question is to figure out How does the speed vary during this period? How does the speed change during this period? We need to choose one answer out of these four options At this point why don't you pause the video read the options and and give this one a try first All right, hopefully you have given this a shot now Let's try to show all of this with a diagram. So at t equals to zero we have a particle Let's let's take a ball. We have a ball which is moving with a velocity of plus five and an acceleration of Plus one. So first, let's decide which direction can we take as positive which direction is negative Let's say the right direction is the positive direction So velocity of plus five meters per second square that means it is moving to the right with five meters per second And acceleration is one meters per second square Which means acceleration again to the right because both of them are positive This is one meters per second square and at time t not at time t not the ball would be over here And at this point the velocity, we don't know what that is really But we do know that the acceleration decreased from plus one to zero point five meters per second square But this is still positive So I will draw the arrow to the right and this is zero point five meters per second square All right, now let's look at the options. We need to think about how is the speed changing? So the first option says the speed increases and then decreases When does a speed increase and when does a speed decrease speed will increase of any object that is moving speed will increase When the acceleration and the direction of speed or the velocity when both of them are in the same direction So we see that happening at t equals to zero the acceleration is to the right Even the velocity is to the right this acceleration is supporting the velocity. It is increasing the velocity Will slightly increase it will be more than five meters per second at a time instant after t equals to zero So let's say let's say at let's say after one second when t is when t is one and then let's say the ball is somewhere over here Now at this point, we don't really know what the acceleration is how the acceleration is changing But we do know that the velocity at this point Acceleration at t equals to zero was one meters per second square then after one second The speed will increase by one meter per second So now the speed could be could be six meters per second And now maybe the acceleration at this point. Maybe it is less. Maybe it is zero point seven five Meters per second square. It is decreasing, right? So now again after one more second when t is two Then let's say that let's say the ball is over here And now the speed will increase by zero point seven five meters per second in one second So now the speed it became 6.75 meters per second So you see what is happening even when the acceleration is decreasing the speed is still increasing It's not increasing by the same amount because it increased by One meters per second in the first second then it increased by zero point seven five meters per second in the next second That is because the acceleration itself is decreasing So even though the acceleration is decreasing here the speed is still increasing constantly Not increasing by the same amount every other second, but still still increasing So in this journey in this journey the speed will constantly increase and that is only because the acceleration and the velocity They are throughout. They are throughout in the same direction So we can say we can say that speed will really just increase in this journey and generally we can say that speed decreases when Speed decreases when velocity and acceleration when velocity and acceleration Have opposite signs when they have opposite Opposite signs So when one is plus the other is minus there will be decrease in speed So for instance if this one meters per second square was in the opposite direction Then after one second this five meters per second would have become four meters per second Then the speed would have decreased when v and a are in the opposite direction when v and a have opposite signs So the first option is wrong and by the similar by similar reasoning even a second one is wrong The speed is constantly increasing in this journey And it's it will keep on decreasing when v and a have opposite signs throughout So that is not the case in this one. So option d is also wrong Now you can try more questions from this exercise in this lesson And if you're watching on youtube do check out the exercise link which is added in the description