Edexcel A-Level Mathematics AS M1.2.2 Application of Vectors Questions

Practise finding velocity and acceleration changes, then use relative position vectors for bearings, meeting times, distances and shared directions from local M1 evidence.

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
(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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Edexcel A-Level Mathematics AS M1.2.2 Application of Vectors Questions question 1

Question (a)

Question (b)