Pearson Edexcel IAL Mathematics M1.2.2 Application of vectors

Practise applying vectors to displacement, velocity, acceleration and force problems, including ships, particles and time-dependent positions.

Exam points

find velocity or acceleration from changes in position or velocity over time
use relative position vectors to calculate bearings, meeting times or shared directions

[Maximum number: 5]

[In this question i and j are horizontal unit vectors directed due east and due north respectively.]

A particle P moves with constant acceleration $(-\lambda \mathbf{i}+2 \lambda \mathbf{j}) \mathrm{ms}^{-2}$ , where $\lambda$ is a positive constant.

At time t=0, the velocity of P is $(5 \mathbf{i}-8 \mathbf{j}) \mathrm{m} \mathrm{s}^{-1}$

(a)

Find the velocity of P when $t=5 \mathrm{~s}$ , giving your answer in terms of i, j and $\lambda$ .

The speed of P when $t=5 \mathrm{~s}$ is $13 \mathrm{~ms}^{-1}$

[ 2 ]

$(5 \mathbf{i}-8 \mathbf{j})+5(-\lambda \mathbf{i}+2 \lambda \mathbf{j})\left(\mathrm{m} \mathrm{s}^{-1}\right)$ isw

M1 A1

(2)

(b)

Show that

25 \lambda^{2}-42 \lambda-16=0

[ 3 ]

$13=\sqrt{(5-5 \lambda)^{2}+(-8+10 \lambda)^{2}}$

M1 A1

$169=25-50 \lambda+25 \lambda^{2}+64-160 \lambda+100 \lambda^{2}$ $25 \lambda^{2}-42 \lambda-16=0^{*}$

A1* cso

(3)

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M1.2.2 - Application of vectors question 1

Question (a)

Question (b)