A particle P of mass 0.4 kg moves under the action of a single constant force F newtons. The acceleration of P is (6i + 8j) m s² . Find (a) the angle between the acceleration and i, (b) the magnitude of F. At time t seconds the velocity of P is v m s⁻¹. Given that when t = 0, v = 9i − 10j, (c) find the velocity of P when t = 5.

A-Level Edexcel Maths Mechanics Newtons Second Law: A particle P of mass 0.4 kg move

A particle P of mass 0.4 kg moves under the action of a single constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2008 - Paper 1

Question 3

A particle P of mass 0.4 kg moves under the action of a single constant force F newtons. The acceleration of P is (6i + 8j) m s² . Find (a) the angle between the ac... show full transcript

Worked Solution & Example Answer:A particle P of mass 0.4 kg moves under the action of a single constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2008 - Paper 1

Step 1

the angle between the acceleration and i

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Answer

To find the angle θ between the acceleration vector and the i direction, we can use the tangent function. The acceleration vector is given as:

$a = 6i + 8j$

Thus,

$an(θ) = \frac{8}{6}$
$θ = \tan^{-1}(\frac{8}{6})$

Calculating this yields:

$θ = 53^{\circ}$

Step 2

the magnitude of F

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Answer

We can find the force F using Newton's second law, which states that:

$F = ma$

Here, the mass m = 0.4 kg and the acceleration a = (6i + 8j) m s².

Calculating the force:

$F = 0.4(6i + 8j) = 2.4i + 3.2j$

To find the magnitude of F, we use the formula:

$|F| = \sqrt{(2.4)^2 + (3.2)^2}$

Calculating this:

$|F| = \sqrt{5.76 + 10.24} = \sqrt{16} = 4$

Step 3

find the velocity of P when t = 5

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Answer

The velocity of P at time t is given by:

$v = 9i - 10j + (6i + 8j)t$

Substituting t = 5:

$v = 9i - 10j + (6i + 8j) \cdot 5$

This simplifies to:

$v = 9i - 10j + (30i + 40j)$

Combining the terms:

$v = (9 + 30)i + (-10 + 40)j = 39i + 30j$

Thus, the velocity of P when t = 5 is:

$v = 39i + 30j ext{ (m s}^{-1}\text{)}$

A particle P of mass 0.4 kg moves under the action of a single constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2008 - Paper 1

Worked Solution & Example Answer:A particle P of mass 0.4 kg moves under the action of a single constant force F newtons - Edexcel - A-Level Maths Mechanics - Question 3 - 2008 - Paper 1

the angle between the acceleration and i

the magnitude of F

find the velocity of P when t = 5

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