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4 Unit A2 2: Applied Mathematics (A-level only)

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Question 48

At time t t\,t seconds a particle P P\,P has acceleration a=[(3t2−4)i+(2t2+4t)j]\mathbf{a} = \left[(3t^2 - 4)\mathbf{i} + (2t^2 + 4t)\mathbf{j}\right]a=[(3t2−4)i+(2t2+4t)j] m s−2^{-2}−2.

When t=3t = 3t=3 the velocity of P P\,P is (10i+20j)(10\mathbf{i} + 20\mathbf{j})(10i+20j) m s−1^{-1}−1.

a.

Find an expression for the velocity of P P\,P in terms of ttt.

[4]
b.

Initially P P\,P is at the point with position vector (2i−5j)(2\mathbf{i} - 5\mathbf{j})(2i−5j) m. Find an expression for the position vector of P P\,P in terms of ttt.

[4]
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4 Unit A2 2: Applied Mathematics (A-level only) Questions

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