OK, so you’ve got to grips with the SUVAT equations, you’re on top of resolving forces, you understand that $F=ma$ and you have M1 under control… only for them to start throwing $\bi$s and $\bj$s around. Who ordered those?

Maybe you have a vague recollection of vectors from GCSE - although it’s quite possible you learnt the two tricks you were expected to do at that level and promptly forgot about them; in fact, your GCSE knowledge probably won’t help all that much (except to help you notice that vectors are what the bold letters represent.)

There’s good news

A good deal of what you need to do for M1 vector questions simply involves treating $\bi$ and $\bj$ as constants - you can get a long way without worrying about “this is east and this is north”. You can - almost - use the SUVAT equations and $\bb{F} = m\bb{a}$ as they stand ((I’ve bolded the $F$ and the $a$. Those are vectors, because forces and acceleration have direction, while mass doesn’t.)) For example, if you know the mass of a particle is 4kg and its acceleration is $-3\bi + 7\bj$, you can simply multiply the two together to get the force: $\bb{F} = m\bb{a} = 4(-3\bi + 7\bj) = -12\bi + 28\bj$. Easy as.

Similarly, you can use the SUVAT equations (apart from one) just the same way: if you know a particle’s acceleration is $\bb{a} = 2\bi - 3\bj$, has initial speed $\bb{u} = -7\bi + 24\bj$ and travels for 2 seconds, its displacement is simply $\bb{s} = \bb{u}t + \frac{1}{2} \bb{a}t^2$ ((All of the SUVAT variables are vectors apart from time.)).

That gives $\bb{s} = (-7\bi + 24\bj)\times 2 + \frac{1}{2} \left(2\bi -3\bj\right)\times 2^2 = (-14\bi + 48\bj) + (4\bi - 6\bj) = -10\bi + 42\bj$ (by grouping the $\bi$s together and the $\bj$s together.)

Sometimes you’ll have variables in there too - often a $t$ - but you work with them just like normal variables.

What’s the SUVAT equation you can’t use?

Good question: it’s the one where you try to square vectors: $v^2 = u^2 + 2as$. There is a vector version, but you need to know something about scalar products first - the dot product you come across in C4. Because there are two ways to multiply vectors, it doesn’t make sense to square a vector, but you can find the scalar product of a vector with itself. The last SUVAT equation becomes:

$\bb{v} \cdot \bb{v} = \bb{u} \cdot \bb{u} + 2 \bb{a} \cdot \bb{s}$