7. Two forces F₁ and F₂ act on a particle P - Edexcel - A-Level Maths Mechanics - Question 7 - 2016 - Paper 1

To find the speed of particle P at t = 3 seconds, we use the kinematic equation relating initial velocity, acceleration, and time:

$v = u + at$

Where:

• $u = (3i - 22j)$ m s⁻¹ (initial velocity)
• $a = (3i + 9j)$ m s⁻² (acceleration)
• $t = 3$ seconds

Substituting the known values:

$v = (3i - 22j) + (3i + 9j) imes 3$

Now calculate the acceleration term:

$3i + 9j$

Expansion results in:

$v = (3 + 3(3))i + (-22 + 9(3))j$

This leads to: $v = (3 + 9)i + (-22 + 27)j$

To find the magnitude of the velocity vector:

$|v| = \sqrt{(12)^2 + (5)^2}$

Calculating the magnitude:

$|v| = \sqrt{144 + 25} = \sqrt{169} = 13 ext{ m/s}$

Therefore, the speed of P when t = 3 seconds is 13 m/s.