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M1 Differentation Questions watch

1. Ok, I've got M1 integration sorted. And I've pretty much figured out M1 differentiation. I just want to be sure I'm doing it right, so could somebody do me a favour and answer these 3 questions and I would be very grateful. Could you also show me the working too.

1) Given that x = t/\3 + 4t + 6, find expressions for v and a in terms of t. Find the displacement, velocity and acceleration when t=2.

2) Given that v = t/\2 - 12t + 40, find the velocity when acceleration is zero.

3) An insect flies in a straight line from one flower to another. The flowers are 270 cm apart and the flight takes 3 seconds. At time t seconds after teh flight begins, the insect is x cm from the first flower. Two alternative models are proposed:

(A) x = 60t/\2 - 10t/\3,
(B) x = 40t/\3 - 10t/\4

For each of these models,

(a) Show that the model fits the information given about the flight,
(b) Find the maximum velocity of the insect,
(c) Sketch the (t,v) graph.

Comment on the differences between the two models. Which do you consider to be the better model?

Thanks in advance to those who help.
2. Presumably x is the same as s?

1)
v = 3t^2 + 4
a = 6t

when t =2

x = 22
v = 16
a = 12

2)
a = 2t -12
2t -12 = 0
2t = 12
t = 6

sub t =6 into v

v = 4

(I've done it mentally, use a calc to check)
3. Ok this question is giving me grief too.

Question:

Given that x = 3 + 20t - t/\4, find expressions for v and a in terms of t. Find the displacement, velocity and acceleration when t = 1 and when t = 3.

I end up with a negative velocity when t = 3 which doesn't make logical sense in my brain that somehow between t = 1 and t = 3 the vehicle has gone from 16m/s to -61m/s. This doesn't make sense since whatever positive number you plug into the formula for acceleration between 1 and 3, you can't get a negative number.
4. (Original post by Mat666)
Presumably x is the same as s?

1)
v = 3t^2 + 4
a = 6t

when t =2

x = 22
v = 16
a = 12

2)
a = 2t -12
2t -12 = 0
2t = 12
t = 6

sub t =6 into v

v = 4

(I've done it mentally, use a calc to check)
Thanks that's excellent. I understand the basics now, it's just the dam mega ultra 10 mark question (number 3 in my first post) that annoys the hell out of me, and questions that don't make sense to my brain (the one in my second post) but at least you cleared out most of the mess in my head.
5. Given that x = 3 + 20t - t/\4, find expressions for v and a in terms of t. Find the displacement, velocity and acceleration when t = 1 and when t = 3.

v = -4t^3 + 20
a = -12t^2

when t=1

v = 16
a = -12

when t=3

v = -88
a = -108

That doesn't look right, but I can't see where I've gone wrong.
6. (Original post by Mat666)
Given that x = 3 + 20t - t/\4, find expressions for v and a in terms of t. Find the displacement, velocity and acceleration when t = 1 and when t = 3.

v = -4t^3 + 20
a = -12t^2

when t=1

v = 16
a = -12

when t=3

v = -88
a = -108

That doesn't look right, but I can't see where I've gone wrong.
I think that's right myself. I got muddled with my negative signs and that's why I ended up with an answer that looked even more wrong, but I'd say that you've got a pretty good answer there.
7. (Original post by Eye Jay)
3) An insect flies in a straight line from one flower to another. The flowers are 270 cm apart and the flight takes 3 seconds. At time t seconds after teh flight begins, the insect is x cm from the first flower. Two alternative models are proposed:

(A) x = 60t/\2 - 10t/\3,
(B) x = 40t/\3 - 10t/\4

For each of these models,

(a) Show that the model fits the information given about the flight,
(b) Find the maximum velocity of the insect,
(c) Sketch the (t,v) graph.

Comment on the differences between the two models. Which do you consider to be the better model?

Thanks in advance to those who help.
Can anybody have a crack at this question now? I know the last part is not possible but the first two parts would be appreciated.
8. thats the trouble with m1, you have to guess if you're right or not. Even more so with m2...

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