Velocity, Acceleration and Displacement time graphs.

[unknown physicist]

Homework Statement

Sketch velocity vs time, acceleration vs time and displacement vs time graphs describing the following motions.a) An object begins at rest and accelerates at a constant rate to a velocity of 5.0 m/s [E]. The object continues along at this velocity.

b) A car accelerates from 0 to 60 km/hr at a constant rate and then hits a wall slowing to a stop almost immediately.

Homework Equations

Suvat equations

The Attempt at a Solution

I am not sure how to solve them at all. How do I figure out the shape of the graph mathematically? I am not sure on how to start.

 

[kuruman]

Hi unknown physicist and welcome to pF.

I am not sure on how to start.

Start with the SUVAT equations that you quoted. Instead of writing the acronym, write down the actual equations and take a good look at them to see how they relate to what is being asked.

 

[cnh1995]

Welcome to PF!
You are supposed to make an attempt at a solution when posting in the HW forum.

a) An object begins at rest and accelerates at a constant rate to a velocity of 5.0 m/s [E]. The object continues along at this velocity.

Which equation would you use for this?

 

[unknown physicist]

Welcome to PF!
You are supposed to make an attempt at a solution when posting in the HW forum.

Which equation would you use for this?

v=u+at ?

 

[cnh1995]

v=u+at ?

Right. Modify this equation by putting the value of u. What shape will the modified equation give?

 

[unknown physicist]

Right. Modify this equation by putting the value of u. What shape will the modified equation give?

v=u+at
u=0
v=at (mx), slope with a 0 y-intercept.

What about the other part?

 

[cnh1995]

v=at (mx), slope with a 0 y-intercept.

Yes. Until??

What about the other part?

Again, start with the equation describing the scenario.

 

[unknown physicist]

Yes. Until??

Again, start with the equation describing the scenario.

Got it, Thanks. But, what about for the acceleration and displacement time graphs? How do I know what numbers to plug in?

 

[cnh1995]

Got it, Thanks. But, what about for the acceleration and displacement time graphs? How do I know what numbers to plug in?

The shape of acceleration vs time graph is mentioned in the problem itself. Read again carefully.
For displacement vs time graph, make use of the known graphs. What is the mathematical relation between displacement and velocity? Which SUVAT equation will you use?

 

[unknown physicist]

The shape of acceleration vs time graph is mentioned in the problem itself. Read again carefully.
For displacement vs time graph, make use of the known graphs. What is the mathematical relation between displacement and velocity? Which SUVAT equation will you use?

s=1/2(u+v)t ?

 

[unknown physicist]

The shape of acceleration vs time graph is mentioned in the problem itself. Read again carefully.
For displacement vs time graph, make use of the known graphs. What is the mathematical relation between displacement and velocity? Which SUVAT equation will you use?

Mentioned in the problem? I can't seem to understand that.

 

[cnh1995]

s=1/2(u+v)t ?

No.
The equation should be s as a function of t. All the other terms should be known constants.

 

[cnh1995]

Mentioned in the problem? I can't seem to understand that.

An object begins at rest and accelerates at a constant rate to a velocity of 5.0 m/s

 

[unknown physicist]

No.
The equation should be s as a function of t. All the other terms should be known constants.

so, I should use s=ut+1/2at^2?

Also, it accelerates at a constant rate, but why does the graph need to go downward? why doesn't it go up like a slope? (for acceleration)?

 

[cnh1995]

so, I should use s=ut+1/2at^2?

Yes. It is in the form y=ax+bx². What is this shape? Put the value of u and see.

but why does the graph need to go downward?

It doesn't. Acceleration is constant w.r.t.time. How would you show this graphically?

 

[unknown physicist]

Yes. It is in the form y=ax+bx². What is this shape? Put the value of u and see.

It doesn't. Acceleration is constant w.r.t.time. How would you show this graphically?

It is a quadratic, so it should be curved.

w.r.t time?

But acceleration will be a straight line, then go straight down, to an acceleration of 0, then it will continue to be 0. That is what the answer sheet shows. I can't understand why it is straight, and why it goes down.

 

[cnh1995]

But acceleration will be a straight line, then go straight down, to an acceleration of 0, then it will continue to be 0.

Yes, after v becomes 5m/s. I was talking about the acceleration period.

It is a quadratic, so it should be curved.

Yes. Which curve is y=bx²?

 

[unknown physicist]

Yes, after v becomes 5m/s. I was talking about the acceleration period.

Yes. Which curve is y=bx²?

yes, I can't seem to understand the acceleration part. Why is it a straight line? then why does it go down?

 

[unknown physicist]

Yes, after v becomes 5m/s. I was talking about the acceleration period.

Yes. Which curve is y=bx²?

the curve will be the s=1/2ut^2
because (u)(t) = 0

 

[cnh1995]

yes, I can't seem to understand the acceleration part. Why is it a straight line? then why does it go down?

It is a straight line (parallel to time axis) because it is "constant" w.r.t. time. Hence, the straight line will have zero slope.

the curve will be the s=1/2ut^2
because (u)(t) = 0

Yes. What is the name of that curve? Look up "conic sections".

 

[unknown physicist]

It is a straight line (parallel to time axis) because it is "constant" w.r.t. time. Hence, the straight line will have zero slope.

Yes. What is the name of that curve? Look up "conic sections".

What do you mean by w.r.t?
and how do I understand it mathematically?

 

[cnh1995]

What do you mean by w.r.t?
and how do I understand it mathematically?

w.r.t. stands for "with respect to". Say the acceleration is constant at 5m/s². Then you'll write a=5. What shape does a=5 give?

 

[unknown physicist]

w.r.t. stands for "with respect to". Say the acceleration is constant at 5m/s². Then you'll write a=5. What shape does a=5 give?

Hold on,
so for the acceleration vs time graph.
u =0
and a is a constant. ( for the first part)

How would I know what to plug for the v=u+at equations?
How would I know that the numbers i'll be plugging in is different that the ones above?

I think I can understand the displacement, and velocity graphs. Just not the acceleration ones.

 

[unknown physicist]

w.r.t. stands for "with respect to". Say the acceleration is constant at 5m/s². Then you'll write a=5. What shape does a=5 give?

for acceleration, I used v =u+at
and I said u=0
a=0
and v=5

I plugged them into the equation and got 5=0? what does that mean?
and then for the second part I said u= 5 and v=5 and plugged them and got 5=5??

 

[cnh1995]

How would I know what to plug for the v=u+at equations?

You should first calculate everything on paper and then plot the graphs. I am not sure I understand your question clearly.

 

[cnh1995]

Ah..I got what you are saying. In the actual problems, the data is not sufficient, so you can't compute anything on paper. You are just expected to draw the shapes of the graphs.

 

[unknown physicist]

Ah..I got what you are saying. In the actual problems, the data is not sufficient, so you can't compute anything on paper. You are just expected to draw the shapes of the graphs.

For acceleration vs time graphs, can I consider acceleration to be 0 while computing?

 

[unknown physicist]

Ah..I got what you are saying. In the actual problems, the data is not sufficient, so you can't compute anything on paper. You are just expected to draw the shapes of the graphs.

Yeah, visualizing them is a bit difficult, I excel in the calculation part. Interpreting them is a bit difficult.

 

[cnh1995]

For acceleration vs time graphs, can I consider acceleration to be 0 while computing?

No. It is non zero when the body is accelerating and becomes zero when the body reaches a velocity of 5m/s. In fact, IMO you are not expected to compute anything on paper.

 

[unknown physicist]

No. It is non zero when the body is accelerating and becomes zero when the body reaches a velocity of 5m/s. In fact, IMO you are not expected to compute anything on paper.

so how do you suggest i solve them?

 

[cnh1995]

so how do you suggest i solve them?

They can't be solved on paper. The data given is not sufficient. Just draw the shapes and that would be sufficient.