Question

A vehicle accelerates with o.4m/s Square . calculate the time taken by the vehicle to increase its speed from 20m/s to 40 m/s

Answer 1

$\boxed{\sf{\green{Time\:taken\:(t) = \bf{50s}}}}$

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Explanation :

$\begin{gathered}\begin{gathered}\underline{\bf\dag{\underline{Given}}}\begin{cases} & \sf{Acceleration\:(a)\:of\;a\:vehicle = \bf{12\;m/s^{2}}} \\ \\ & \sf{Initial\:velocity\:(u)\;of\;a\:vehicle = \bf{20\;m/s}}\\ \\ & \sf{Final\:velocity\:(v)\;of\;a\:vehicle = \bf{40\;m/s}} \end{cases} \end{gathered}\end{gathered}$

$\underline{\bf\dag{\underline{To\:Find}}:}$

★Time taken (t) by the vehicle to increase it's speed from 20m/s to 40m/s = ?

$\underline{\bf\dag{\underline{Solution}}:}$

★ Using first eqⁿ of motion :-

$\qquad\quad\bf\dag\:\bigg\lgroup {\sf {\pink{v = u + at }}}$

★ Putting all known values :-

$\qquad\longrightarrow\quad\sf 40 = 20 + 0.4t$

$\qquad\longrightarrow\quad\sf 20 = 0.4t$

$\qquad\longrightarrow\quad\sf \dfrac{20\:\times 10}{0.4}$

$\qquad\longrightarrow\quad\sf \dfrac{200}{4}$

$\qquad\longrightarrow\quad\sf \dfrac{\cancel{200}}{\cancel{4}}$

$\qquad\longrightarrow\quad{\bf{\purple{t = 50s}}}$

$\small\therefore\:{\underline{\sf{Hence,\:time\:taken\:to\:increase\:it's\:speed\:is\:\bf{50s.}}}}$

′

$\underline{\bf\dag{\underline{More\:to\:know}}:}$

★ Three equations of motion :-

v = u + at ㅤㅤㅤㅤㅤ[Used above]

s = ut + (1/2) at²

v² = u² + 2as

★ Some important definitions :-

Acceleration

Acceleration is the process where velocity changes. Since, velocity is the speed and it has some direction. So, change of velocity is considered as acceleration.

Initial velocity

Initial velocity is the velocity of the object before the effect of acceleration.

Final velocity

After the effect of acceleration, the velocity of object changes, the new velocity gained by the object velocity is known as final velocity.

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