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# Tutor profile: Youssef H.

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Youssef H.
Senior Mechanical Engineering student
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## Questions

### Subject:Physics (Newtonian Mechanics)

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Question:

A 40,000 kg train car travelling at 8 m/s towards another stationary train car. upon collision, they couple together and move along at 5 m/s. Find the mass of the second train car?

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Youssef H.

The main concept in this question is conservation of momentum; the summation of momenta of the two train cars before collision equals the momentum of the couple after collision. This can be mathematically represented as follows: \$\$m_1*v_1+m_2*v_2 = (m_1+m_2)*v_t\$\$ \$\$m_1, v_1 \$\$ and \$\$v_2\$\$ are given, and hence, the only unknown in the above equation is \$\$m_2\$\$ Substituting the given values for \$\$m_1, v_1 \$\$ and \$\$v_2\$\$: \$\$40,000*8+m_2*0 = (40,000+m_2)*5\$\$ \$\$320,000 = 200,000 + 5m_2\$\$ \$\$320,000 -200,000 = + 5m_2=120,000\$\$ \$\$m_2=120,000/5=24,000 kg\$\$

### Subject:Calculus

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Question:

\$\$ f(x) = x^4 + x^2 - 8x\$\$ Find \$\$f''(2)\$\$.

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Youssef H.

The question asks for the second derivative of the given function at 2. First, we should get the first derivative. Then, we differentiate it. Lastly, we plug in 2 for x in the second derivative. \$\$f'(x) = 4x^3 + 2x - 8\$\$ \$\$f''(x) = 12x^2 + 2\$\$ \$\$f''(2) = 12(2)^2 + 2=48+2=50\$\$

### Subject:Algebra

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Question:

\$\$ x + 2 y = 8 \$\$ \$\$ 2x - y = 6 \$\$ Quantity A Quantity B \$\$x \$\$ \$\$x \$\$ Given the above two equations, determine whether A is greater than B, B is greater than A, A and B are equal, or there is not enough information to determine.

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Youssef H.

By multiplying the second equation by 2 and summing up the two equations, \$\$ 5x = 20 \$\$, which means \$\$x = 4\$\$. By substituting in any of the two equations, \$\$y=2\$\$. Hence, quantity A is greater.

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