1 of 8 0-day streak

Reconstruct quantities from their rates

Question 1 of 8

No calculator

Use the rate model and the boundary value to reconstruct the quantity

A collection vessel has capacity 500 L

Time t is measured in min. The model is valid only for 0 ≤ t ≤ 5. Q is the volume in litres, and its signed net rate is in L/min

Q'(t)=t+2

Q(0)=40

Find the volume at 4 min

(a)1 mark

Which quantity and unit are recovered by anti-differentiating this supplied rate?

Elapsed time in minutes

Volume in litres

Volume in litres per minute squared

Volume rate in litres per minute

(b)3 marks

Let P(t) be the anti-derivative with zero constant term. The physical quantity will be P(t)+C after applying the supplied value

Enter every coefficient in descending powers, including zero for an absent term

P(t)=A_2t^{2}+A_1t+A_0

\(\text{coefficient of }t^{2}\) \(\text{coefficient of }t\) \(\text{constant coefficient}\)

Find the additive constant C from the supplied quantity value

Exact value

(d)1 mark

Select the specific quantity rule satisfying both the rate and the supplied value

Q(t)=-\frac{1}{2}t^{2}-2t+40

Q(t)=\frac{1}{2}t^{2}+2t+40

Q(t)=t+2

Q(t)=\frac{1}{2}t^{2}+2t+41

(e)1 mark

Enter the requested volume, in L

Exact value