Question

a vehicle accelerates with 0.4m/^2 calculate the time taken by the vehicle to increase its speed 20m/s to 40m/s

Answer 1

Gɪᴠᴇɴ :-

• Initial velocity (u) = 20m/s
• Final velocity (v) = 40m/s
• Acceleration (a) = 0.4m/s²

ᴛᴏ ғɪɴᴅ :-

• Time taken (t)

sᴏʟᴜᴛɪᴏɴ :-

By using ,

1st equation of motion , we get

• v = u + at

Put all the given values in it, we get

➮ 40 = 20 + 0.4t

➮ 0.4t = 40 - 20

➮ 0.4t = 20

➮ t = 20/0.4

➮ t = 50s

Hence,

• Time taken (t) by the vehicle is 50s.

ᴇǫᴜᴀᴛɪᴏɴs ᴏғ ᴍᴏᴛɪᴏɴ :-

• 1) v = u + at
• 2) s = ut + ½at²
• 3) v² - u² = 2as

where,

• v = final velocity
• u = initial velocity
• s = displacement
• t = time taken
• a = acceleration

Answer 2

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

$\red{\overline {\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

Explanation :

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

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

• 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 :-

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

★ Putting all known values :-

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

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

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

$\qquad\longrightarrow\quad\sf \dfrac{20}{0.4} = t$

$\qquad\longrightarrow\quad\sf \dfrac{20\:\times\:10}{0\not{.}4} = t$

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

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

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

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

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

★ Three equations of motion :-

1. v = u + at ㅤㅤㅤㅤㅤ[Used above]
2. s = ut + (1/2) at²
3. 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.

$\red{\overline {\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$