Edexcel IAL M1 Vectors (Mechanics context) Questions
Position, velocity and force vectors in i, j form; magnitude and direction; r = r₀ + vt for constant velocity; resultant forces.
- M1 · Mechanics 1
- Calculator allowed
- 41 practice questions
What the questions test
The 41 M1 vectors (mechanics context) practice questions cover:
Worked example 1
Ship A starts at position $(0, 5)$ relative to a port and moves with a constant velocity vector of $\begin{pmatrix} 3 \\ -1 \end{pmatrix}\text{ km h}^{-1}$. Ship B starts at $(4, 0)$ and moves with a constant velocity vector of $\begin{pmatrix} 1 \\ 2 \end{pmatrix}\text{ km h}^{-1}$.
- Write down the position vectors of Ship A and Ship B at time $t$ hours.
- Find an expression for the square of the distance between the ships at time $t$, denoted $D^2(t)$.
- Find the exact time $t$ when the two ships are closest to each other.
Mark scheme
- M1 for writing the vector equations of motion.
A1 for $\mathbf{r_A} = \begin{pmatrix} 3t \\ 5-t \end{pmatrix}$ and $\mathbf{r_B} = \begin{pmatrix} 4+t \\ 2t \end{pmatrix}$. - M1 for finding the relative displacement vector $\mathbf{r_B} - \mathbf{r_A} = \begin{pmatrix} 4 - 2t \\ 3t - 5 \end{pmatrix}$.
M1 for setting up the square of the magnitude: $D^2(t) = (4 - 2t)^2 + (3t - 5)^2$.
A1 for expanding and simplifying to a quadratic: $D^2(t) = 16 - 16t + 4t^2 + 9t^2 - 30t + 25 = 13t^2 - 46t + 41$. - M1 for recognizing that minimum distance occurs when the derivative of $D^2(t)$ is zero (or using the vertex formula $t = -b/2a$).
M1 for solving $26t - 46 = 0 \implies 26t = 46$.
A1 for finding exactly $t = \frac{23}{13}$ hours.
Worked example 2
A drone is programmed to fly in a straight line. Its position vector \(r\) (in km) at time \(t\) (in hours) is \(r = \begin{pmatrix} -5 \\ 12 \end{pmatrix} + t \begin{pmatrix} 8 \\ -6 \end{pmatrix}\).
Calculate the exact speed of the drone in km h^{-1}, and find its distance from the origin at \(t=2\).
Mark scheme
Velocity vector \(v = \begin{pmatrix} 8 \\ -6 \end{pmatrix}\). Speed \(= |v| = \sqrt{8^2 + (-6)^2} = \sqrt{64+36} = 10\) km h^{-1}. M1A1
Position at \(t=2\): \(r(2) = \begin{pmatrix} -5 \\ 12 \end{pmatrix} + 2 \begin{pmatrix} 8 \\ -6 \end{pmatrix} = \begin{pmatrix} 11 \\ 0 \end{pmatrix}\). M1A1
Distance from origin \(= \sqrt{11^2 + 0^2} = 11\) km. M1A1
FAQ
What vectors (mechanics context) is in Edexcel IAL M1?
Position, velocity and force vectors in i, j form; magnitude and direction; r = r₀ + vt for constant velocity; resultant forces.
Is M1 a calculator paper?
Yes, a calculator is allowed in M1, but method marks are only given for working you write down.
How are M1 vectors (mechanics context) questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.