Calculus Questions Help!!

[Jacktenstar]

I am in Year 10 and doing some revision for a Calculus test.

1. If the position of a particle moving in a straight line is given by the rule x(t)=-2t^2 +8t +3, where x is in centimetres and t is in seconds, find:

f) the distance travelled in the first 3 seconds

By subsituting in 0 and 3 for (t) in the original function, I thought the distance travelled was 6cm/sec but the answer says it is 10cm/sec. Any idea where I went wrong?


5.Find the maximum possible volume of a fully enclosed cylindrical water tank given that the total internal surface area of the tank is 600 PI square units

I tried setting out both formulas: A=PIr^2h and 600 PI =2PIr^2 + 2PIrh and then divided both sides by PI and eventually canceled down to get 300= r^2 +rh, but I couldn't figure out how to go further. Any ideas how to solve?

Thanks for any help that can be given

[Galapagos]

I am in Year 10 and doing some revision for a Calculus test.

1. If the position of a particle moving in a straight line is given by the rule x(t)=-2t^2 +8t +3, where x is in centimetres and t is in seconds, find:

f) the distance travelled in the first 3 seconds

By subsituting in 0 and 3 for (t) in the original function, I thought the distance travelled was 6cm/sec but the answer says it is 10cm/sec. Any idea where I went wrong?

I got the same answer as you by plugging in the initial position minus the position at 3 seconds...but I've only done differential calculus so there is probably a hole in my knowledge regarding this question?

5.Find the maximum possible volume of a fully enclosed cylindrical water tank given that the total internal surface area of the tank is 600 PI square units

I tried setting out both formulas: A=PIr^2h and 600 PI =2PIr^2 + 2PIrh and then divided both sides by PI and eventually canceled down to get 300= r^2 +rh, but I couldn't figure out how to go further. Any ideas how to solve?

Thanks for any help that can be given

Volume = πr^2h

and Area = 2[πr^2] + 2πrh

Follow the steps on this page http://brainmass.com/math/calculus/217259,.

[Miss World]

why the hell is it under HSC Mathematics 2u course?

[Jacktenstar]

Anyone able to explain it clearly. As we have not done any calculus questions using 2 separate equations before. That explanation in the URL was also hard to understand.

Thanks in advance

[Galapagos]

Mate these questions are way above Year 10 level. Google it or something until you find the answers.

[Jacktenstar]

Mate these questions are way above Year 10 level. Google it or something until you find the answers.

Strange how it is in the textbook for calculus we were given by the teacher that we have been working through, if it is above the level expected of a year 10 student or even early year 11.

I will just ask the teacher then, how to do it. He can explain to me how to do these type questions if we are expected to know this for our in-class unit-tests.

Thanks anyway

[nsbored]

You have distance (or displacement) confused with speed (or velocity). Distance is measured in cm not cm/sec.

The distance travelled will be taken from the starting position to each turning point and back to the end.

The particle will turn when its velocity is zero, so you need to derive this displacement function, make equal to zero and solve. This will give you t = 2.

x(0) = 3
x(2) = 11
x(3) = 9

It travels 8 cm in the positive direction for 2 seconds, turns and travels a further 2 cm in the negative direction. Total distance travelled is 10 cm.