A single force with x-component Fₓ acts on a 2.0 kg object as it moves along the x-axis. A graph of Fₓ versus t is shown in FIGURE P5.32. Draw an acceleration graph aₓ versus t) for this object.

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Hi everyone in this practice problem, we will have a net force directed purely in the right direction applied on a kg card that costs parallel to the axis. The force time graph is provided in the problem statement in a figure where the time is in seconds and fy or force is in Newton from point negative 10 to 0. The force is going from 0 to 20 Newton from 0.0 to 30 seconds. The force is going from 20 to Newton and between 30 50 seconds, the force is going constantly at 40 Newton. We're being asked to work out the acceleration time graph of the cart. And the way we want to tackle this is to by utilizing Newton's second law. So according to Newton's second law, F will be equals to m multiplied by a or force will be equals to the mass multiplied by its acceleration. Therefore, the acceleration at any given time can be obtained by taking the force and dividing it by the mass. So we now looking at our graph that is given for the force versus time, we can note some notable points so that we can then um make our own acceleration versus time graph. So the first point that we're going to note is the negative 10 point comma zero here and then zero comma 20 then uh 30 comma 40 and then lastly comma 40. So there will be four different uh points that we're gonna note. So let's first look into the first one which is going to be negative 10 seconds and zero Newton. So converting this or converting our force into uh acceleration, we will be doing essentially dividing our force with the mass which is given to be 10 kg. So mass is 10 kg and we wanna just defy all the forces in the points. It with the 10 kg to obtain our point for the acceleration graph. So negative 10 seconds and zero Newton and then zero seconds and 20 Newton and then next is going to be 30 seconds and 40 Newton and then lastly is 50 seconds and 40 Newton just like so and then let's actually uh divide all the forces. So the first point is going to be negative 10 seconds and zero Newton divided by 10 kg which will obtain the point of negative seconds and 0 m per second squared. And then for the second one, it's going to be zero seconds and comma 20 Newton divided by 10 kg which will give us the point of zero seconds and 2 m per second squared. And for the 3rd 3rd point, we'll have 30 seconds coma, 40 Newton divided by 10 kg, which will then obtain the point of 30 seconds. Comma 4 m per second squared. Lastly, for our last point, we will have uh 50 seconds comma 40 Newton divided by 10 kg which will obtain the point of 50 seconds, comma 4 m per second squared just like so awesome. So now what we need to do next is to just graph the acceleration diagram or acceleration graph. So let's take the um black color pen and I'm just gonna start with drawing our vertical and horizontal axis here. And I am going to then put all the axis Y and X and the Y axis is going to be our acceleration, which is just going to be a in meters per second squared. And then the X axis is just going to be our time B in seconds. And then if we are looking at all the points that we have, the time is still going to be the same, which is going to be in increments of uh 10 seconds. So I'm going to essentially just uh take our uh Y axis and move it a little bit to the right to make it easier for us. And I'm going to draw the Y uh the X axis here in increments of 10 seconds up until 50 seconds. So negative 10 seconds, 10 seconds, 20 seconds, 30 seconds, 30 seconds and 50 seconds, we don't really need the second here. I was just uh putting it there just so that you guys are not confused, but I'm going to delete that now and this is going to be our X axis looking into the Y axis which is going to be our acceleration. The acceleration is going to range from 0 to 4. So I'm just gonna do this in increments of one. So 1234 and then five, 1234 and then five. So let's start by actually um taking all the points or pointing all or drawing all the points. We first have the negative 10 seconds and 0 m per second squared. So that will be here and then moving into zero seconds, it will be 2 m per second squared. So we wanna uh graph that point and then moving into 30 seconds, it will be 4 m per second squared. So this is going to be a little harder. So I'm just gonna actually um take this uh line horizontally to make sure that we are going to draw it. Uh Well, so we have at 30 seconds, it's going to be at 4 m per second. Acceleration and at 50 seconds, it's still going to be staying at 4 m per second just like so awesome. So after we draw all the points, we just want to actually connect all the points. So I'm connecting this uh negative 10 seconds and comma 0 m per seconds. And then I'm gonna connect that with zero comma 2 m per second squared. And then I'm going to connect the zero comma two with 30 comma four and then lastly the 30 comma four with 50 comma four. So that will be the final acceleration versus time graph here and that will be it for this video. So if you guys still have any sort of confusion, please feel free to check out our other lesson videos on similar topics available on our website. But other than that, the rat graph is going to be representing the progression of acceleration through time and I just deleted the blue helpful line earlier to make it clearer for you guys to see. So that'll be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar topics available on our website. But other than that, that will be it for this video. Thank you so much for watching. Bye bye.

A single force with x-component Fₓ acts on a 2.0 kg object as it moves along the x-axis. A graph of Fₓ versus t is shown in FIGURE P5.32. Draw an acceleration graph aₓ versus t) for this object.

Verified Solution

Key Concepts

Newton's Second Law of Motion

Force vs. Time Graphs

Acceleration