The forces $F_1=4\mathbf{\text{i}}+2\mathbf{\text{j}}$ N and $F_2=2\mathbf{\text{i}}-\mathbf{\text{j}}$ N act on a particle.

Find the resultant force.

A resultant force of $(2\mathbf{\text{i}}+3\mathbf{\text{j}})$ N acts on a particle of mass $3$ kg, causing it to accelerate.

Find the acceleration of the particle in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.

The forces $F_1=-3\mathbf{\text{i}}+6\mathbf{\text{j}}$ N and $F_2=3\mathbf{\text{i}}-a\mathbf{\text{j}}$ N act on a particle which is in equilibrium.

Find the value of $a$.

A resultant force of $(2\mathbf{\text{i}}+3\mathbf{\text{j}})$ N acts on a particle of mass $m$ kg, causing it to accelerate at $(10\mathbf{\text{i}}+15\mathbf{\text{j}})$ m s${}^{-2}$.

Find the mass of the particle.

A resultant force $\mathbf{\text{F}}$ N acts on a particle of mass $1.5$ kg, causing it to accelerate at $(6\mathbf{\text{i}}+8\mathbf{\text{j}})$ m s${}^{-2}$.

Find an expression for $\mathbf{\text{F}}$ in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.

A resultant force $\mathbf{\text{F}}$ N acts on a particle of mass $2$ kg, causing it to accelerate at $(1.5\mathbf{\text{i}}-2\mathbf{\text{j}})$ m s${}^{-2}$.

Find an expression for $\mathbf{\text{F}}$ in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.

A resultant force of $(3\mathbf{\text{i}}-2\mathbf{\text{j}})$ N acts on a particle of mass $2$ kg, causing it to accelerate.

Find the acceleration of the particle in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.

The forces $F_1=5\mathbf{\text{i}}+\mathbf{\text{j}}$ N and $F_2=\mathbf{\text{i}}+\mathbf{\text{j}}$ N and $F_3$ act on a particle which is in equilibrium.

Find the force $F_3$.

A resultant force of $(4\mathbf{\text{i}}+\mathbf{\text{j}})$ N acts on a particle of mass $m$ kg, causing it to accelerate at $(8\mathbf{\text{i}}+2\mathbf{\text{j}})$ m s${}^{-2}$.

Find the mass of the particle.

Two forces, ${\mathbf{\text{F}}}_1=(2\mathbf{\text{i}}+\mathbf{\text{j}})$ N and ${\mathbf{\text{F}}}_2=(3\mathbf{\text{i}}-2\mathbf{\text{j}})$ N act on a particle of mass $0.5$ kg, causing it to accelerate.

Find the acceleration of the particle in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.

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[Edexcel M1 May 2008 Q3b]

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 s^–2 .

Find the magnitude of F.

(3 marks)

[Edexcel M1 Jan 2012 Q3a]

Three forces F₁, F₂ and F₃ acting on a particle P are given by

F₁ = (7i – 9j) N

F₂ = (5i + 6j) N

F₃ = (pi + qj) N

where p and q are constants.

Given that P is in equilibrium, find the value of p and the value of q.

(3 marks)

[Edexcel M1 Jan 2012 Q3b Edited]

Three forces F₁, F₂ and F₃ acting on a particle P are given by

F₁ = (7i – 9j) N

F₂ = (5i + 6j) N

F₃ = (pi + qj) N

where $p=-12$ and $q=3$.

The force F₃ is now removed. The resultant of F₁ and F₂ is R.
Find the magnitude of R.

(2 marks)

[Edexcel M1 Jan 2012 Q3c Edited]

Three forces F₁, F₂ and F₃ acting on a particle P are given by

F₁ = (7i – 9j) N

F₂ = (5i + 6j) N

F₃ = (pi + qj) N

where $p=-12$ and $q=3$.

The force F₃ is now removed. The resultant of F₁ and F₂ is R.
Find the angle, to the nearest degree, that the direction of R makes with j.

(3 marks)

A resultant force of $(6\mathbf{\text{i}}-9\mathbf{\text{j}})$ N acts on a particle of mass $3$ kg, causing it to accelerate.

Find the magnitude of the acceleration of the particle.
Give your answer correct to 2 significant figures.

Two forces, ${\mathbf{\text{F}}}_1=(9\mathbf{\text{i}}-6\mathbf{\text{j}})$ N and ${\mathbf{\text{F}}}_2=(3\mathbf{\text{i}}-10\mathbf{\text{j}})$ N act on a particle of mass $4$ kg, causing it to accelerate.

Find the acceleration of the particle in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.

Two forces, ${\mathbf{\text{F}}}_1=(3\mathbf{\text{i}}-2\mathbf{\text{j}})$ N and ${\mathbf{\text{F}}}_2=(2\mathbf{\text{i}}-4\mathbf{\text{j}})$ N act on a particle of mass $0.25$ kg, causing it to accelerate.

Find the acceleration of the particle in terms of $\mathbf{\text{i}}$ and $\mathbf{\text{j}}$.