Marco O.

Engineering Graduate student with over 2 years of tutoring experience

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Physics (Newtonian Mechanics)

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Question:

A car starts from rest and accelerates to 20 m/s, with constant acceleration, in the span of 10 seconds. It continues for 30 seconds and then decelerates back to rest. How far did the car travel?

Marco O.

Answer:

We can break this problem in to multiple parts to solve it: acceleration, constant velocity, and deceleration. In all cases, we will use one of Newton's equations of motion to solve it. Constant velocity: d = v*t 20 m/s * 30 s = 600 m Acceleration: First we find the acceleration. a = (v2 - v1)/t = (20 m/s - 0)/10s = 2m/s/s Now we can find the distance traveled d = v_1 * t + .5* a * t^2 = 0*10s + .5 * 2m/s/s * 10*10 = 100 m Deceleration: First we find the acceleration. a = (v2 - v1)/t = (0 - 20m/s)/10s = -2m/s/s Now we can find the distance traveled d = v_2 * t + .5* a * t^2 = 20*10 - .5 * 2m/s/s * 10*10 = 100 m The total distance traveled would be 800 m.

Calculus

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Question:

Integrate the following expression: xe^x

Marco O.

Answer:

We have to use integration by parts to integrate this expression. ∫ u*dv = u*v - ∫ v*du ∫ u*dv = ∫ xe^x dx u = x du=dx dv = e^x dx v = e^x ∫ xe^x dx = x*e^x - ∫ e^x dx = x*e^x - e^x

Calculus

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Question:

Find the first and second derivative of the following expression: 3x*cos(x)

Marco O.

Answer:

Using the chain rule with x as one part and cos(x) as the other First: 3cos(x) - 3x*sin(x) Second: -3x*cos(x) - 6sin(x)

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