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Science Physics library One-dimensional motion Acceleration. Airbus A take-off time. Airbus A take-off distance. Why distance is area under velocity-time line. What are velocity vs. Acceleration vs. What are acceleration vs. Practice: Acceleration and velocity. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript - [Instructor] All right, I wanna talk to you about acceleration versus time graphs because as far as motion graphs go, these are probably the hardest.
One reason is because acceleration just naturally is an abstract concept for a lot of people to deal with and now it's a graph and people don't like graphs either particularly often times. Another reason is, if you wanted to know the motion of the object, let's say it was this doggie. This is my doggie Daisy. Let's say Daisy was accelerating. If you wanted to know the velocity that daisy had, you can't figure it out directly from this graph unless you have some extra information.
You have to know information about the velocity Daisy had at some moment in order to figure out from this graph the velocity Daisy had at some other moment.
So, what can this graph tell you about the motion of Daisy? Well, let's say this graph described Daisy's acceleration. So Daisy can be accelerating. Maybe we're playing catch. We'll give her a ball. We'll throw the ball. Hopefully she actually lets go and she brings it back. This graph is gonna represent her acceleration. So this graph, we just read it, it says that Daisy had two meters per second squared of acceleration for the first four seconds and then her acceleration dropped to zero at six seconds and then her acceleration came negative until it was negative three at nine seconds.
But, from this we can't tell if she's speeding up or slowing down. Well, we can figure out some stuff because acceleration is related to velocity and we can figure out how it's related to velocity by remembering that it is defined to be the change in velocity over the change in time.
So this is how we make our link to velocity. So if we solve this for delta v, we get that the delta v, the change in velocity over some time interval, will be the acceleration during that time interval times interval itself, how long did that take.
This is the key to relating this graph to velocity. In other words, let's consider this first four seconds. Let's go between zero and four seconds. Daisy had an acceleration of two meters per second squared. So that means, well, two was the acceleration meters per second squared, times the accel, times the time, excuse me, the time was four seconds. So there was four seconds worth of acceleration.
You get positive eight. What are the units? This second cancels with that second. You get positive eight meters per second. So the change in velocity for the first four seconds was positive eight. This isn't the velocity. It's the change in velocity. How would you ever find that for this diagonal region. This is as problem. Look at this. If I wanted to find, let's say the velocity at six seconds, well the acceleration at this point is two but then the acceleration at this point is one.
The acceleration at this point is zero. That acceleration we keep changing. How would I ever figure this out? What acceleration would I plug in during this portion? But we're in luck. This formula allows us to say something really important. A geometric aspect of these graphs that are gonna make our life easier and the way it makes our life easier is that, look at what this is.
This is saying acceleration times delta t, but look it. The acceleration we plug in was this, two. So for the first four seconds, the acceleration was two. The time, delta t, was four. We took this two multiplied by that four and got a number, positive eight, but this is a height times the width. If you take height times width, that just represents the area of a rectangle. So all we found was the area of this rectangle.
The area is giving us our delta v because area, right, of a rectangle is height times width. We know that the height is gonna represent the acceleration here and the width is gonna represent delta t. Just by the definition of acceleration we arranged, we know that a times delta t has to just be the change in velocity. Explanation: There is no such case. An object with a constant acceleration but zero velocity is not possible, because according to the definition of acceleration, acceleration is the rate of change in velocity.
If an object is at zero velocity it does mean that it is at rest. Which of the following velocity-time graphs shows a realistic situation for a body in motion? Solution : Except graph b , other graphs show more than one velocity of the particle at single instant of time which is nit possible for realistic situation.
In realistic situation, the body cannot have more than one velocity at the same instant OR in other words, each axis vertical with time axis must intersect the curve only at once. Here in this question, it is given that acceleration is constant or the body moves with a uniform acceleration. Therefore as per the relation obtained we can say that, the graph should be a parabola which should be symmetric about the x-axis.
The rate of acceleration is constant. If we draw distance time graph for uniform motion then it will be straight line. For better understanding we can take an example, a car is running at a constant speed say 20 metres per second, will cover equal distances of 20 metres, every second, so its motion will be uniform. The other name of negative acceleration is Retardation or Deceleration. A deceleration is opposite to the acceleration.
A positive acceleration means an increase in velocity with time. When the car slows down, the speed decreases. When an object is speeding up, the acceleration is in the same direction as the velocity. Yes if the body is travelling with uniform speed in a circular track its speed remains the same but the velocity is non-uniform as the direction of the body is changing every time. As we know, velocity is a vector quantity, so as the direction of motion changes, velocity also changes.
No change in speed or direction is experienced. And it follows that the acceleration is zero. No, a body can not have its velocity constant, while its speed varies. Rather, it can have its speed constant and its velocity varying.
For example in a uniform circular motion. Acceleration that does not change in time is called uniform or constant acceleration. In a velocity versus time graph for uniform acceleration, the slope of the line is the acceleration. Average acceleration refers to the rate at which the velocity changes. To understand the graph of the acceleration vs time graph you must have an idea about some terminologies.
Let us discuss these terminologies first. Acceleration:- It is the ratio of the change in velocity in the given time interval. In simple words acceleration means to gain and lose the velocity of the vehicle. Velocity:- The velocity of an object is defined as the ratio of the change in the position of the object in the given time interval. Time period:- The time period is defined as the interval of the time given to perform the specific activity.
The area under the graph gives the change in the velocity of the object in the given interval of the time.
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