What Does a Non-Uniformly Accelerated Motion Graph Look Like?

[Saitama]

Hello Everyone!
Just got a homework about graphs of motion. I have solved all the problems but got stuck in one of them. Here's the problem:-

I solved it like this:-
0 to t1 - Uniform Motion with negative velocity
t1 to t2 - Rest
t2 to t3 - Uniformly retarded

I asked my teacher and he told me that the last step is wrong i.e. t2 to t3 is wrong.
Would someone please tell me where i am wrong?
Thanks...

 

[Andrew Mason]

I asked my teacher and he told me that the last step is wrong i.e. t2 to t3 is wrong.
Would someone please tell me where i am wrong?

What information does the slope of the graph give you? Since the slope from t2-t3 is changing (decreasing) what kind of motion is this? Is slope changing at a uniform rate? How can you tell?

AM

 

[Saitama]

Thanks Andrew for your Reply.
I just wanted to know that if it is uniformly accelerated or uniformly retarded. It should be uniformly retarded because Displacement-time graph for uniformly retarded is same as it is given in t2-t3. But here its starting from velocity 0(zero) and a body cannot retard because velocity is 0. If the body will try to move too, its velocity will increase only. In no sense it can decrease. But also it cannot be uniformly accelerated motion because if we draw tangents at different points of the slope between t2 to t3, we will notice that the velocity is decreasing so it cannot be uniformly accelerated.

 

[gneill]

The displacement at t = t3 would appear to be less than the maximum displacement achieved in the period t2 <= t <= t3. If that is so, more than simple friction (retardation?) is at work.

The object "takes off" from its rest position at t = t2 at some velocity (as evidenced by the sudden change in slope of the curve at that time), after which the rate of change in displacement slows and eventually reverses direction. What kind of motion does this remind you of?

 

[Andrew Mason]

Thanks Andrew for your Reply.
I just wanted to know that if it is uniformly accelerated or uniformly retarded. It should be uniformly retarded because Displacement-time graph for uniformly retarded is same as it is given in t2-t3. But here its starting from velocity 0(zero) and a body cannot retard because velocity is 0. If the body will try to move too, its velocity will increase only. In no sense it can decrease. But also it cannot be uniformly accelerated motion because if we draw tangents at different points of the slope between t2 to t3, we will notice that the velocity is decreasing so it cannot be uniformly accelerated.

Why do you think it is uniform? What is the shape of the graph? Following up on Gneill's post, what does that tell you about how S changes with t?

AM

 

[Saitama]

One thing more i can add, the time between t1 and t2 is equal to t2 and t3.
Now any answers?

 

[Andrew Mason]

One thing more i can add, the time between t1 and t2 is equal to t2 and t3.
Now any answers?

It looks to me that the graph from t2-t3 is an arc of a circle. That does not mean that the path is circular - we are only dealing with motion in one dimension. What you have to do is determine the acceleration that would be required to make that graph. hint: if it was a parabolic graph, what would be the second derivative of displacement with respect to time (ie. the acceleration). Since it is not a parabola, can the acceleration be the same as with a parabola?

AM

 

[Saitama]

Thanks Andrew for your reply.
I got my homework on the basis of those graphs only which I have studied.
Till now I have studied Uniform Motion graphs, Uniformly accelerated graphs, Uniformly Reatarded and Non-Uniformly Accelerated graphs. Is the graph in the question one of these?

 

[Andrew Mason]

So what does the graph of non-uniformly accelerated motion look like?

AM