Question

if u=2i-2j+3k and the final velocity is v=2i-4j+5k and it is covered in a time of 10sec then acceleration is

Answer 1

Answer:

$\bullet\:\tt u = 2 \hat{i} - 2\hat{j} + 3\hat{k}$

$\bullet\:\tt v= 2 \hat{i} - 4\hat{j} + 5\hat{k}$

Concept : Rate of change of velocity per unit time is known as Acceleration.

$\longrightarrow\rm a= \dfrac{\Delta v}{ t}$

$\longrightarrow\rm a= \dfrac{ v - u}{ t}$

$\longrightarrow\rm a= \dfrac{(2 \hat{i} - 4\hat{j} + 5\hat{k}) - (2 \hat{i} - 2\hat{j} + 3\hat{k})}{10}$

$\longrightarrow\rm a= \dfrac{2 \hat{i} - 4\hat{j} + 5\hat{k}- 2 \hat{i} + 2\hat{j} - 3\hat{k}}{10}$

$\longrightarrow\rm a= \dfrac{ - 2\hat{j} + 2\hat{k} }{10}$

$\longrightarrow\rm a= \dfrac{ \sqrt{(- 2 )^{2} + 2 ^{2} } }{10}$

$\longrightarrow\rm a= \dfrac{ \sqrt{4+ 4} }{10}$

$\longrightarrow\rm a= \dfrac{ \sqrt{2 \times 2+ 2 \times 2} }{10}$

$\longrightarrow\rm a= \dfrac{ 2 + 2 }{10}$

$\longrightarrow\rm a= \dfrac{4}{10}$

$\longrightarrow\rm a= \dfrac{2}{5}$

$\longrightarrow\underline{\boxed{\bold{a= 0.4 \: {ms}^{ - 2}} }}$

Answer 2

Answer⤵️

$\frac{1}{5} ( - i + j)$

Acceleration:-

$\huge= \frac{(v - u)}{t}$

$a = \frac{(2i - 4j + 5k) - (2i - 2j + 3k)}{10} \\ a = \frac{( - 2j + 2k)}{10} \\ a = \frac{ - 1}{5}i \: + \: \frac{1}{5}j \\ a = \frac{1}{5} ( - i + j)$

Hope this helps!

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