Mechanics

A firework takes off from ground level, accelerating upwards for 10s with constant acceleration 4m/s^2.
Sketch the displacement time graph.
So I did u= 0, so v= u+at, v= 40m/s, s=vt-1/2at^2, s=200m. Is this correct way of doing the calculation?

(edited 3 years ago)

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Reply 1

RogerOxon

Original post by Shas72

Where did the v=40 and s=200 come from?

I'd use

s=ut+\frac{at^2}{2}

to get points for the sketch.

(edited 3 years ago)

Reply 2

Shas72

Original post by RogerOxon

Where did the v=40 and s=200 come from?

By using v=u+at

Reply 3

Shas72

Original post by RogerOxon

Where did the v=40 and s=200 come from?

I'd use

s=ut+\frac{at^2}{2}

to get points for the sketch.

Is there a diff method that I can use for plotting the graph?

Reply 4

RogerOxon

Original post by Shas72

By using v=u+at

You don't need to calculate v before s. As per my edit above:

Original post by RogerOxon

I'd use

s=ut+\frac{at^2}{2}

to get points for the sketch.

You should be able to deduce its shape from the equation.

Reply 5

Shas72

Original post by RogerOxon

You don't need to calculate v before s. As per my edit above:

You should be able to deduce its shape from the equation.

Iam not having problems in plotting or sketching the graph. My problem is I'm not able to understand what formulas to use to get to the values

Reply 6

Shas72

Original post by RogerOxon

You don't need to calculate v before s. As per my edit above:

You should be able to deduce its shape from the equation.

So is it that we know u=0 in this case, t=10s and A= 4m/s^2, so we make use of the formula that has these ?

Reply 7

RogerOxon

Original post by Shas72

Iam not having problems in plotting or sketching the graph. My problem is I'm not able to understand what formulas to use to get to the values

You are asked to sketch a time-displacement graph, i.e. t and s. You know that u=0 (t=0). You want the simplest formula for s, when you know u, a and t.

Reply 8

RogerOxon

Original post by Shas72

So is it that we know u=0 in this case, t=10s and A= 4m/s^2, so we make use of the formula that has these ?

Yes. Look through the equations that you have, and see which is the most direct for what you want. When u=0, that simplifies many of them.

Reply 9

Shas72

Original post by RogerOxon

You are asked to sketch a time-displacement graph, i.e. t and s. You know that u=0 (t=0). You want the simplest formula for s, when you know u, a and t.

Thanks that was very helpful. I was doing all unnecessary stuff of finding v

Reply 10

Shas72

Original post by RogerOxon

Yes. Look through the equations that you have, and see which is the most direct for what you want. When u=0, that simplifies many of them.

Yeah you are right!!! Thanks!!!

Reply 11

RogerOxon

Original post by Shas72

Thanks that was very helpful. I was doing all unnecessary stuff of finding v

Good. It should simplify to the same forumula, but will add extra steps, with the associated possibility of mistakes.

Reply 12

Shas72

Original post by RogerOxon

Good. It should simplify to the same forumula, but will add extra steps, with the associated possibility of mistakes.

Yeah true

Reply 13

RogerOxon

Original post by Shas72

Yeah true

Just for fun:

s=vt-\frac{at^2}{2}

v=u+at

\therefore s=(u+at)t-\frac{at^2}{2}=ut+at^2-\frac{at^2}{2}=ut+\frac{at^2}{2}

Reply 14

Shas72

Original post by RogerOxon

Good. It should simplify to the same forumula, but will add extra steps, with the associated possibility of mistakes.

Can you pls advise on this one .
A ball is thrown upwards from a point 1m above the ground with initial speed 5m/s. It accelerates downwards at a constant rate of 10m/s^2 until it stops moving upwards, when it is caught by someone standing on a ladder.
Sketch the graph
According to what you have advised, s=1m, u=5m/s, a=10m/s^2, v=0 as it stops.
Should I use the same formula?

Reply 15

RogerOxon

Original post by Shas72

Be careful with your signs. The acceleration and initial speed are in different directions.

You also need to be careful about where you're measuring s from. All SUVAT equations implicitly have s=0 at t=0.

There are different ways of approaching this - it's all about the one that is simplest or makes the most sense to you.

As your goal is to sketch the graph, and you know that the ball is caught when v=0 (vertically), you can quickly get the time for that. Can you see how?

I would use that time to calculate s. Which SUVAT equation (knowing u, v=0, a and t) is the simplest?