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###### AS maths question help

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5 years ago

Hi, could someone please help with this:

A bird leaves its nest at time t = 0 for a short flight along a straight line. The bird then returns to its nest. The bird is modelled as a particle moving in a straight horizontal line. The distance, s metres, of the bird from its nest at time t seconds is given by s = 1/10 (t^4 – 20t^3 + 100t^2), where 0 ≤ t ≤10 (a) Explain the restriction, 0 ≤ t≤ 10.

I really dont understand this question. could someone help please?

A bird leaves its nest at time t = 0 for a short flight along a straight line. The bird then returns to its nest. The bird is modelled as a particle moving in a straight horizontal line. The distance, s metres, of the bird from its nest at time t seconds is given by s = 1/10 (t^4 – 20t^3 + 100t^2), where 0 ≤ t ≤10 (a) Explain the restriction, 0 ≤ t≤ 10.

I really dont understand this question. could someone help please?

Reply 1

5 years ago

Original post by Bertybassett

Hi, could someone please help with this:

A bird leaves its nest at time t = 0 for a short flight along a straight line. The bird then returns to its nest. The bird is modelled as a particle moving in a straight horizontal line. The distance, s metres, of the bird from its nest at time t seconds is given by s = 1/10 (t^4 – 20t^3 + 100t^2), where 0 ≤ t ≤10 (a) Explain the restriction, 0 ≤ t≤ 10.

I really dont understand this question. could someone help please?

A bird leaves its nest at time t = 0 for a short flight along a straight line. The bird then returns to its nest. The bird is modelled as a particle moving in a straight horizontal line. The distance, s metres, of the bird from its nest at time t seconds is given by s = 1/10 (t^4 – 20t^3 + 100t^2), where 0 ≤ t ≤10 (a) Explain the restriction, 0 ≤ t≤ 10.

I really dont understand this question. could someone help please?

Well, the bird flies away from its nest and comes back. How far away is the bird when $t=0$? So the restriction must mean that...?

Reply 2

5 years ago

Original post by RDKGames

Well, the bird flies away from its nest and comes back. How far away is the bird when $t=0$? So the restriction must mean that...?

well it would be zero metres away? but i dont get what im meant to write for 3 marks.

Reply 4

5 years ago

Original post by Bertybassett

well it would be zero metres away? but i dont get what im meant to write for 3 marks.

Yeah, though I meant $t=10$.

You just need to say that the restriction is when the function is +ve, so this covers the entire journey of the bird.

Distance cannot be -ve by definition, so must only count the function where it's +ve.

Reply 5

1 year ago

Original post by Bertybassett

Hi, could someone please help with this:

A bird leaves its nest at time t = 0 for a short flight along a straight line. The bird then returns to its nest. The bird is modelled as a particle moving in a straight horizontal line. The distance, s metres, of the bird from its nest at time t seconds is given by s = 1/10 (t^4 – 20t^3 + 100t^2), where 0 ≤ t ≤10 (a) Explain the restriction, 0 ≤ t≤ 10.

I really dont understand this question. could someone help please?

A bird leaves its nest at time t = 0 for a short flight along a straight line. The bird then returns to its nest. The bird is modelled as a particle moving in a straight horizontal line. The distance, s metres, of the bird from its nest at time t seconds is given by s = 1/10 (t^4 – 20t^3 + 100t^2), where 0 ≤ t ≤10 (a) Explain the restriction, 0 ≤ t≤ 10.

I really dont understand this question. could someone help please?

Part a:

When t = 0, s = 0 too. That means Displacement is 0 when the bird is at rest.

When t = 10, s = 0 again. That means the bird flew for 10 seconds and came back to the nest in 10 seconds, therefore the displacement is 0 as it returned.

Part b:

S = 1/10(t⁴-20t³+100t²)

Expand the brackets and get s = 1/10t⁴-2t³+10t²

Differentiate S to get v, because the velocity is 0 when the bird first comes to rest.

ds/dt = 2/5t³-6t²+20t

So v = 2/5t³-6t²+20t

Put v = 0:

2/5t³-6t²+20t = 0

t = 0, t = 5 and t = 10

T must be 5 because the other two values of t are when the bird is at rest and when the bird comes back.

Substitute in the value of t = 5 into the S equation:

s = 1/10((5)⁴-20(5)³+100(5)²) = 62.5m

You're welcome 😂❤️

Original post by Shamsul.17

Original post by Shamsul.17

Part a:

You're welcome

You're welcome

This thread is 3 years old! Please don't resurrect old threads, and do not post solutions - it is against the rules of the forum. Thanks

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