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Help Pls

Anyone know how to do the following question? Thanks.

Screenshot 2021-10-12 at 9.31.23 PM.png
Reply 1
Avatar for awc14
awc14
13
Hello,

For part a you have the equation for the velocity of the particle when t = 5. If you integrate this in terms of t you have the equation for the displacement of the particle, so just plug t = 5 into this.


For part b, you want to work out the displacement of the particle in the next second. You need to use the second equation for this, as the first is not true for t > 5. If you integrate this equation, then plug in t = 1 you have worked out the displacement of the particle in the next second. Add your answer from part a to this and you have worked out the total displacement from 0 to 6s.

Hope this made sense!
(edited 2 years ago)
Reply 2
Avatar for mqb2766
mqb2766
21
Original post by awc14
Hello,

For part a you have the equation for the velocity of the particle when t = 5. If you differentiate this in terms of t you have the equation for the displacement of the particle, so just plug t = 5 into this.


For part b, you want to work out the displacement of the particle in the next second. You need to use the second equation for this, as the first is not true for t > 5. If you differentiate this equation, then plug in t = 1 you have worked out the displacement of the particle in the next second. Add your answer from part a to this and you have worked out the total displacement from 0 to 6s.

Hope this made sense!

^^^ This, but integrate rather than differentiate.
Reply 3
Avatar for awc14
awc14
13
Original post by mqb2766
^^^ This, but integrate rather than differentiate.

Thank you, how stupid of me
Reply 4
Avatar for josefgas5
josefgas5
OP
9
Original post by awc14
Hello,

For part a you have the equation for the velocity of the particle when t = 5. If you integrate this in terms of t you have the equation for the displacement of the particle, so just plug t = 5 into this.


For part b, you want to work out the displacement of the particle in the next second. You need to use the second equation for this, as the first is not true for t > 5. If you integrate this equation, then plug in t = 1 you have worked out the displacement of the particle in the next second. Add your answer from part a to this and you have worked out the total displacement from 0 to 6s.

Hope this made sense!

hello,
I got 76.6m for part a. Is that right?
For part b, I'm not sure what to sub in (t=?) to find C in the second equation.
Reply 5
Avatar for mqb2766
mqb2766
21
Original post by josefgas5
hello,
I got 76.6m for part a. Is that right?
For part b, I'm not sure what to sub in (t=?) to find C in the second equation.

a) looks good
https://www.wolframalpha.com/input/?i=integrate+t*sqrt%2814%2B2t%5E2%29+from+0+to+5

b) when t=5, the curves must join so s=76.6. which gives C
Reply 6
Avatar for josefgas5
josefgas5
OP
9
Original post by mqb2766
a) looks good
https://www.wolframalpha.com/input/?i=integrate+t*sqrt%2814%2B2t%5E2%29+from+0+to+5

b) when t=5, the curves must join so s=76.6. which gives C

I got 109.9m for the final displacement. Can anyone confirm if its correct or not? Thanks
Reply 7
Avatar for mqb2766
mqb2766
21
Original post by josefgas5
I got 109.9m for the final displacement. Can anyone confirm if its correct or not? Thanks

https://www.wolframalpha.com/input/?i=integrate+1000%2Ft%5E2+from+5+to+6
You can use "learn" to use it, it is quite simple and useful.
You obviously add C to that.
Reply 8
Avatar for josefgas5
josefgas5
OP
9
Original post by mqb2766
https://www.wolframalpha.com/input/?i=integrate+1000%2Ft%5E2+from+5+to+6
You can use "learn" to use it, it is quite simple and useful.
You obviously add C to that.


Thank you!!

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