In taking off, an aircraft moves on a straight runway AB of length 1.2 km. The aircraft moves from A with initial speed 2 m s⁻¹. It moves with constant acceleration and 20 s later it leaves the runway at C with speed 74 m s⁻¹. Find (a) the acceleration of the aircraft, (b) the distance BC.

A-Level Edexcel Maths Mechanics Constant Acceleration - 1D: In taking off, an aircraft moves

In taking off, an aircraft moves on a straight runway AB of length 1.2 km - Edexcel - A-Level Maths Mechanics - Question 1 - 2005 - Paper 1

Question 1

In taking off, an aircraft moves on a straight runway AB of length 1.2 km. The aircraft moves from A with initial speed 2 m s⁻¹. It moves with constant acceleration ... show full transcript

Worked Solution & Example Answer:In taking off, an aircraft moves on a straight runway AB of length 1.2 km - Edexcel - A-Level Maths Mechanics - Question 1 - 2005 - Paper 1

Step 1

(a) the acceleration of the aircraft

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Answer

To find the acceleration of the aircraft, we can use the equation of motion:

$v = u + at$

Here:

$v = 74\, \text{m/s}$ (final velocity)
$u = 2\, \text{m/s}$ (initial velocity)
$t = 20\, \text{s}$ (time)

Substituting the values into the equation:

$74 = 2 + a \times 20$

Rearranging gives:

$a = \frac{74 - 2}{20} = \frac{72}{20} = 3.6\, \text{m/s}^2$

Thus, the acceleration of the aircraft is $3.6\, \text{m/s}^2$ .

Step 2

(b) the distance BC

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Answer

To find the distance BC (the distance covered after leaving point C), we first need to find the distance covered on the runway AC using the equation:

$s = ut + \frac{1}{2}at^2$

Where:

$u = 2\, \text{m/s}$ (initial velocity)
$t = 20\, \text{s}$ (time)
$a = 3.6\, \text{m/s}^2$ (acceleration)

Substituting the values:

$AC = 2 \times 20 + \frac{1}{2} \times 3.6 \times (20)^2$

Calculating each part:

First part: $2 \times 20 = 40$ m
Second part: $\frac{1}{2} \times 3.6 \times 400 = 720$ m

Thus,

$AC = 40 + 720 = 760\, \text{m}$

Now, to find the distance BC:

The total length of runway AB is $1.2\, \text{km}$ or $1200\, \text{m}$ .

Therefore, distance BC is:

$BC = AB - AC = 1200 - 760 = 440\, \text{m}$

In taking off, an aircraft moves on a straight runway AB of length 1.2 km - Edexcel - A-Level Maths Mechanics - Question 1 - 2005 - Paper 1

Worked Solution & Example Answer:In taking off, an aircraft moves on a straight runway AB of length 1.2 km - Edexcel - A-Level Maths Mechanics - Question 1 - 2005 - Paper 1

(a) the acceleration of the aircraft

(b) the distance BC

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