First slide

Motion in two and three dimensions

Question

The initial velocity of a particle is $u = (4 \hat{i} + 3 \hat{j}) {ms}^{- 1}$ . It is moving with uniform acceleration $a = (0 .4 \hat{i} + 0 .3 \hat{j}) {ms}^{- 2}$ . The magnitude of its velocity after 10 s is

Moderate

A

3 ms^-1
B

4 ms^-1
C

5 ms^-1
D

10 ms^-1

Solution

$v = u + at = (4 \hat{i} + 3 \hat{j}) + (0 .4 \hat{i} + 0 .3 \hat{j}) \times 10 = (8 \hat{i} + 6 \hat{j}) {ms}^{- 1}$
The x and y components of velocity are v_x = 8 ms^-1 and v_y= 6 ms^-1.
The magnitude of velocity $v = \sqrt{v_{x}^{2} + v_{y}^{2}} = \sqrt{(8)^{2} + (6)^{2}} = 10 {ms}^{- 1}$

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