Neco 2018 Mathematics Question 10

Practice essay / theory question 10 from the 2018 Neco Mathematics examination. This question covers Variation .

Neco 2018 Mathematics Essay / Theory

Topic: Variation

Question 10 NECO • 2018 • MATHEMATICS • essay

The time \(T\) (in seconds) required for a particle to travel a distance \(s\) metres under a force that varies directly as the square of its speed \(v\) (in m s⁻¹) and inversely as its mass \(m\) (in kg) is described by a joint variation. In addition, the speed \(v\) varies inversely as the square root of the distance travelled. When the mass is \(2\) kg and the distance is \(8\) m, the time taken is \(4\) s.

( a )

Express the relationship between \(T\), \(v\) and \(m\) using a constant of variation \(k\).

( b )

Write the relationship between \(v\) and \(s\) using a constant \(c\).

( c )

Using the information given (\(m=2\) kg, \(s=8\) m, \(T=4\) s), determine the combined constant \(K\) in the expression \(T = \frac{K}{sm}\).

( d )

Find the time taken when the mass is \(5\) kg and the distance travelled is \(18\) m. Give your answer as a simplified fraction.

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This is Neco 2018 Mathematics Question 10. It is one of the essay questions from the 2018 Neco Mathematics examination.

The question covers Variation .

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