A vehicle, of total mass 1200 kg, is travelling along a straight, horizontal road at a constant speed of 13 m s⁻¹. This vehicle begins to accelerate at a constant rate. After 40 metres it reaches a speed of 17 m s⁻¹. Find the resultant force acting on the vehicle during the period of acceleration.

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A vehicle, of total mass 1200 kg, is travelling along a straight, horizontal road at a constant speed of 13 m s⁻¹ - AQA - A-Level Maths Pure - Question 13 - 2021 - Paper 2

Question 13

A vehicle, of total mass 1200 kg, is travelling along a straight, horizontal road at a constant speed of 13 m s⁻¹. This vehicle begins to accelerate at a constant r... show full transcript

Worked Solution & Example Answer:A vehicle, of total mass 1200 kg, is travelling along a straight, horizontal road at a constant speed of 13 m s⁻¹ - AQA - A-Level Maths Pure - Question 13 - 2021 - Paper 2

Step 1

Selects and uses an appropriate constant acceleration equation to find the acceleration.

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Answer

To find the acceleration, we can apply the kinematic equation:

$v^2 = u^2 + 2as$

Where:

$v$ = final velocity = 17 m s⁻¹
$u$ = initial velocity = 13 m s⁻¹
$s$ = displacement = 40 m
$a$ = acceleration

Substituting in the values:

$(17)^2 = (13)^2 + 2a(40)$

This simplifies to:

$289 = 169 + 80a$

Rearranging gives:

$120 = 80a$

Thus, we find:

$a = 1.5 ext{ m s}^{-2}$

Step 2

Substitutes their value of a into F = ma to obtain their F.

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Answer

Using Newton's second law to find the resultant force, we use the equation:

$F = ma$

Where:

$m$ = mass = 1200 kg
$a$ = acceleration = 1.5 m s⁻²

Substituting the values:

$F = 1200 imes 1.5 = 1800 ext{ N}$

Therefore, the resultant force acting on the vehicle during the period of acceleration is 1800 N.

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