In which direction does the acceleration act?

In the direction of the resultant force.

How do you find the resultant of several forces in one direction?

Add them, with forces opposing the chosen direction taken as negative.

A 2 kg particle has resultant force (8\mathbf{i}+4\mathbf{j}) N. Find \mathbf{a}.

(4\mathbf{i}+2\mathbf{j}) m s^{-2}

What does a negative acceleration mean?

The velocity is decreasing in the chosen positive direction (a deceleration).

How do you find acceleration when velocity changes from \mathbf{u} to \mathbf{v} in time t?

\mathbf{a}=\frac{\mathbf{v}-\mathbf{u}}{t} (constant acceleration)

A particle moves at constant velocity. What is \mathbf{F}?

\mathbf{0} (Newton's first law, from \mathbf{F}=m\mathbf{a} with \mathbf{a}=\mathbf{0})

Newton's second law in a straight lineEdexcel A-Level Maths: Flashcards

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State Newton's second law for constant mass.

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State Newton's second law for constant mass.: $\mathbf{F}=m\mathbf{a}$ : resultant force $=$ mass $\times$ acceleration
In which direction does the acceleration act?: In the direction of the resultant force.
What is the unit of force in terms of kg, m and s?: $1$ N $=1$ kg m s $^{-2}$
How do you find the resultant of several forces in one direction?: Add them, with forces opposing the chosen direction taken as negative.
A driving force $D$ and resistance $R$ act on a car of mass $m$ . Write the equation of motion.: $D-R=ma$
A $2$ kg particle has resultant force $(8\mathbf{i}+4\mathbf{j})$ N. Find $\mathbf{a}$ .: $(4\mathbf{i}+2\mathbf{j})$ m s $^{-2}$
A resultant force of $80$ N acts on a $40$ kg sledge. What is its acceleration?: $2$ m s $^{-2}$
What does a negative acceleration mean?: The velocity is decreasing in the chosen positive direction (a deceleration).
Which suvat equation links $v$ , $u$ , $a$ and $s$ without $t$ ?: $v^2=u^2+2as$
How do you find the magnitude of a vector acceleration $(a\mathbf{i}+b\mathbf{j})$ ?: $\sqrt{a^2+b^2}$
How do you find acceleration when velocity changes from $\mathbf{u}$ to $\mathbf{v}$ in time $t$ ?: $\mathbf{a}=\frac{\mathbf{v}-\mathbf{u}}{t}$ (constant acceleration)
A particle moves at constant velocity. What is $\mathbf{F}$ ?: $\mathbf{0}$ (Newton's first law, from $\mathbf{F}=m\mathbf{a}$ with $\mathbf{a}=\mathbf{0}$ )

Exam questions on Newton's second law in a straight line

A sledge of mass $40$ kg is pulled from rest along horizontal ground by a horizontal rope. The tension in the rope is $100$ N and the resistance to motion is a constant $20$ N. Model the sledge as a particle.
Find the distance travelled by the sledge in these $6$ s.2 marks
A particle $P$ of mass $2$ kg is acted on by two forces only, $\mathbf{F}_1=(6\mathbf{i}-4\mathbf{j})$ N and $\mathbf{F}_2=(2\mathbf{i}+8\mathbf{j})$ N, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular unit vectors.
Find the magnitude of the acceleration of $P$ .2 marks
A lorry of mass $8000$ kg travels along a straight horizontal road. The resistance to the lorry's motion is a constant $1200$ N. Model the lorry as a particle.
The driving force of the lorry's engine is $6400$ N. Find the acceleration of the lorry.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).