# M2 help.Watch

#1
A particle P of mass 0.2kg is at rest at a fixed origin O. At time t seconds where 0≦t≦3, a force of (2ti + 3j)N is applied to P.
a) find the position vector of P when t=3
b) When t=3, the force acting on P changes to (6i + (12 - t^2)j)N, where 3
≦t.

I just can't get the same answer as the back of the book for b).

After working out the acceleration, I integrated to get the velocity function:
30ti + (60t - (5t^3)/3 )j +C

To work out C I used the acceleration in a) to get a velocity -> 5t^2 i +15tj.

Then by making t=0 and v= 45i + 45j, I got C=45i + 45j.

Making t=3 in v= (30t+45)i + (60t +45 -(5t^3)/3)j , I get v= (135i + 180j)
The answer on the back states (135i - 90j) which I'm unable to get.

Could any one point me in the right direction? I'll post my working on paper if the above doesn't make sense.

0
4 years ago
#2
(Original post by Whateverisbest)
A particle P of mass 0.2kg is at rest at a fixed origin O. At time t seconds where 0≦t≦3, a force of (2ti + 3j)N is applied to P.
a) find the position vector of P when t=3
b) When t=3, the force acting on P changes to (6i + (12 - t^2)j)N, where 3
≦t.

I just can't get the same answer as the back of the book for b).

After working out the acceleration, I integrated to get the velocity function:
30ti + (60t - (5t^3)/3 )j +C

To work out C I used the acceleration in a) to get a velocity -> 5t^2 i +15tj.

Then by making t=0 and v= 45i + 45j, I got C=45i + 45j.

Making t=3 in v= (30t+45)i + (60t +45 -(5t^3)/3)j , I get v= (135i + 180j)
The answer on the back states (135i - 90j) which I'm unable to get.

Could any one point me in the right direction? I'll post my working on paper if the above doesn't make sense.

Firstly I assume they are asking to find the velocity when t=3, but there's a problem with this. You haven't posted the entire question!

Secondly when you use t=0 when calculating for C the velocity has to be 0 and not 45i + 45j.

For part b) are they asking to find the velocity at t=3? How did you get 45i + 45 j?
0
4 years ago
#3
(Original post by Whateverisbest)
A particle P of mass 0.2kg is at rest at a fixed origin O. At time t seconds where 0≦t≦3, a force of (2ti + 3j)N is applied to P.
a) find the position vector of P when t=3
b) When t=3, the force acting on P changes to (6i + (12 - t^2)j)N, where 3
≦t.

I just can't get the same answer as the back of the book for b).

After working out the acceleration, I integrated to get the velocity function:
30ti + (60t - (5t^3)/3 )j +C

To work out C I used the acceleration in a) to get a velocity -> 5t^2 i +15tj.

Then by making t=0 and v= 45i + 45j, I got C=45i + 45j.

Making t=3 in v= (30t+45)i + (60t +45 -(5t^3)/3)j , I get v= (135i + 180j)
The answer on the back states (135i - 90j) which I'm unable to get.

Could any one point me in the right direction? I'll post my working on paper if the above doesn't make sense.

I used v=u+at in part B and the answer I got was (135i + 90j)

the difference between my answer and the one in the back of your book is the sign between the I and j vectors where I got a + sign and it must be a - sign.

so can you double check the answer in your book, and in case of my answer being correct, I used v=u+at ,where

v: velocity after new force
u: velocity before new force (5t^2i+15tj)
a: acceleration after the mew force [30i+(60-5t^2)j]
t: time (t)

by substituting and simplifying I get v=(5t^2+30t)I+(75t-5t^3)j

by taking t=3

v=135i +90j

0
4 years ago
#4
(Original post by Whateverisbest)
A particle P of mass 0.2kg is at rest at a fixed origin O. At time t seconds where 0≦t≦3, a force of (2ti + 3j)N is applied to P.
a) find the position vector of P when t=3
b) When t=3, the force acting on P changes to (6i + (12 - t^2)j)N, where 3
≦t.

I just can't get the same answer as the back of the book for b).

After working out the acceleration, I integrated to get the velocity function:
30ti + (60t - (5t^3)/3 )j +C

To work out C I used the acceleration in a) to get a velocity -> 5t^2 i +15tj.

Then by making t=0 and v= 45i + 45j, I got C=45i + 45j.

Making t=3 in v= (30t+45)i + (60t +45 -(5t^3)/3)j , I get v= (135i + 180j)
The answer on the back states (135i - 90j) which I'm unable to get.

Could any one point me in the right direction? I'll post my working on paper if the above doesn't make sense.

Hello again

I found that question in my book while I was revising. My book was similar to yours after all.

I already colored your mistakes by red above, but to make it clearer for you I'd explain your mistakes for you.

First of all you have taken t=0 when v=45i+45j ,while you were expected to take t=3, because v is equal to 45i+45j when t is equal to 3. and if you worked that out you'll find c=(-45i-90j) .

Secondly, you mistakenly found v when t=3, while you should have taken t=6, because this is what the question asks for, and if you worked that out, you'll find that v=135i-90j

0
4 years ago
#5
since the force is not constant ( and the mass is constant ) the acceleration is not constant ... so you cannot use SUVAT
0
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