VCE Specialist 3/4 Question Thread!

[Conic]

                     

                     

                     

[M_BONG]

Really quick question..

Am I right in saying that distance travelled is the instantaneous velocity?

[psyxwar]

Really quick question..

Am I right in saying that distance travelled is the instantaneous velocity?

uh... no? Instantaneous velocity is velocity at a specific point in time?

[M_BONG]

uh... no? Instantaneous velocity is velocity at a specific point in time?

Ok soz. that appears to be a really stupid question to ask even for a non-physics student LOL.

What I meant to ask is: why is distance travelled in a time interval equal to the instaneous velocity halfway through the time interval.

Eg. Doing this review question. "A particle travels 30m in the sixth second"

According to solutions, instantaneous speed is 30m/s when t=5.5m but how is that related to the particle travelling 30m in the sixth second?

[lzxnl]

Ok soz. that appears to be a really stupid question to ask even for a non-physics student LOL.

What I meant to ask is: why is distance travelled in a time interval equal to the instaneous velocity halfway through the time interval.

Eg. Doing this review question. "A particle travels 30m in the sixth second"

According to solutions, instantaneous speed is 30m/s when t=5.5m but how is that related to the particle travelling 30m in the sixth second?

This looks like a constant acceleration question.
Travelling 30 m in the sixth second => travels 30 m in the time period 5s to 6s => average speed is 30 m/s
Average speed occurs half way through time period for constant acceleration => average speed of 30 m/s occurs at t = 5.5s

That's what the book meant

[bts]

Find the component of the force (7i + 3j) N in the direction of the vector 2i – j.

i know how they got the ans, but don't quite understand how the force times unit vector times unit vector is the component of the force im looking for?

someone please help!

[allstar]

please excuse my drawing, but how is that 'statement' correct? how would I prove that?

[Phy124]

So you have two vectors and with angle between them.

Form a triangle by joining their "heads" with a vector .

By the cosine rule we have that

We also know that

Thus

Cancelling terms and rearranging yields

[bts]

Find the component of the force (7i + 3j) N in the direction of the vector 2i – j.

i know how they got the ans, but don't quite understand how the force times unit vector times unit vector is the component of the force im looking for?

someone please help!

shouldn't it be f.a . unit vector a?

please help

[keltingmeith]

Find the component of the force (7i + 3j) N in the direction of the vector 2i – j.

i know how they got the ans, but don't quite understand how the force times unit vector times unit vector is the component of the force im looking for?

someone please help!

What they've done is projected the first vector onto the second.

You can think of projections like putting one vector onto a new set of axis, defined by the vector you're projecting onto. In fact, if you project a vector onto i, you'll find that you're just left with the x-component.

[lucas.vang]

Please help with this question also
I'm kinda confused with the vector/scalar resolute concept

Question 4 (HEFFERNAN GROUP 2006)
In the right angle triangle ABC, the hypotenuse is AC = -4i + j
If BC is parallel to the vectore -3i + 2j, find AB

Why do they use the vector resolute?

Thanks in advanced!

[brightsky]

AB is the vector resolute of AC in the direction of -3i + 2j. Let a = AC = -4i + j, and b = -3i + 2j. Then AB = (a.b)/(b.b) b.

[lzxnl]

please excuse my drawing, but how is that 'statement' correct? how would I prove that?

So you have two vectors and with angle between them.

Form a triangle by joining their "heads" with a vector .

By the cosine rule we have that

We also know that

Thus

Cancelling terms and rearranging yields

Here it's assumed implicitly that the length of vector a is sqrt(a.a) and that the dot product is associative and a whole bunch of other properties people take for granted about dot products

Really, you need to start from a definition somewhere. Some people define the dot product as a.b = |a||b| cos theta and then derive Cartesian relations from that

Others define the dot product from the Cartesian expression and show that a.b = |a||b| cos theta
In either case, you can just think of it as a definition that doesn't need to be proved

[M_BONG]

If a question asks: find a vector in the direction of motion of the particle, at t= pi/4.

Do we sub t=pi/4 in the VELOCITY vector or the DISPLACEMENT vector?

I did it in the displacement vector but answer says to sub it in velocity vector. Someone explain please? Pretty stupid way to lose 2 marks tbh....

[kinslayer]

If a question asks: find a vector in the direction of motion of the particle, at t= pi/4.

Do we sub t=pi/4 in the VELOCITY vector or the DISPLACEMENT vector?

I did it in the displacement vector but answer says to sub it in velocity vector. Someone explain please? Pretty stupid way to lose 2 marks tbh....

For a fixed time t, all the displacement vector tells you is where the particle is, nothing else. To find the direction in which the particle is moving, you need to know how the displacement vector varies with time, which is given by the velocity vector.