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# Tutor profile: Hoeyin C.

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Hoeyin C.
MSci Physics Undergraduate at the University of Birmingham
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## Questions

### Subject:Basic Math

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Question:

12 batteries are able to power 24 robots for 16 days. How many batteries are needed to power 8 robots for 32 days?

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Hoeyin C.

We are given the number of batteries required for a certain scenario, which we can compare to our second scenario to work out how many batteries are required. The number of days is doubled from 16 to 32 so we would need 2 times the batteries required in scenario 1. The other change is that now only 8 robots are in need of power. By recognizing that this is a third of the original 24, only a third of the batteries should therefore be required. Combining this with the doubling of the days, we arrive at the answer by doing the calculation: $$12$$(batteries) $$\times$$ $$2 \div 3$$ = 8 batteries. Therefore 8 batteries are required to power 8 robots for 32 days.

### Subject:Calculus

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Question:

Find the derivative of $$f(x) = x^3 + 2x^2 +10$$

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Hoeyin C.

The derivative of a function $$f'(x)$$, helps us to describe the slope/gradient of the function $$f(x)$$. To help solve this question we use the power rule: $$\frac{d}{dx} x^n = nx^{n-1}$$ Going through each part of the calculation, $$\frac{d}{dx} x^3 = 3x^{3-1} = 3x^2$$ $$\frac{d}{dx}2 x^2 = (2\times2)x^{2-1} = 4x$$ $$\frac{d}{dx}10 \equiv \frac{d}{dx}10x^0 = (10\times0)x^{0-1} = 0$$ [where $$\equiv$$ means equivalent to] And so we arrive at the answer: $$f'(x) = 3x^2 + 4x$$

### Subject:Physics

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Question:

Does a heavier object fall faster than a lighter object inside of a vacuum?

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Hoeyin C.

No, this is because of Newton's second law which can be simplified to Force(F) = mass(m) x acceleration(a). The force of gravity on each object is then equivalent to mg (where g is the acceleration due to gravity). Assuming there is no air resistance (vacuum), we can then equate this gravitational force to the right hand side of Newton's second law to get mg = ma. The mass of the object cancels out and we therefore find that a = g for any falling object inside of a vacuum, i.e. all objects fall at the same rate regardless of their mass. If there was air resistance however, then the Force(F) is made up of more than just the gravitational force(mg) and we would have to consider more things (like the surface area of the objects) when calculating the rate at which they fall.

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