Question

The initial velocity of body is 6 m/s and it's acceleration is 2 m/s2. In how much time will it attain a velocity of 20m/s ? How much distance will it travel in this time
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Answer 1

Given

⚠️ Initial velocity = 6 m/s

⚠️ Acceleration = 2 m/s²

⚠️ Final velocity = 20 m/s

To find

⚠️ Time taken to attain that velocity

⚠️ Distance travelled by it during that time

Solution

Here we have ;

⇒ Initial velocity (u) = 6 m/s

⇒ Acceleration (a) = 2 m/s²

⇒ Final velocity (v) = 20 m/s

Now using 1st equation of motion :

✒️ v = u + at

✒️ 20 = 6 + 2t

✒️ 20 - 6 = 2t

✒️ 14 = 2t

✒️ t = 14/2

✒️ t = 7 s

Therefore, time taken to attain that velocity = 7 seconds.

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Now using 2nd equation of motion :

✒️ s = ut + ½ at²

✒️ s = 6 × 7 + ½ × 2 × (7)²

✒️ s = 42 + 49

✒️ s = 91 m

Therefore, distance travelled by it in this time = 91 m.

Answer 2

$\small{\underline{\sf{\pink{Find:\rightarrow}}}}$

• In how much time will it attain a velocity of 20m/s
• Distance covered

$\large{\underline{\sf{\red{Given:\rightarrow}}}}$

• Initial Velocity [u]= 6m/s
• Acceleration [a]= 2m/s²
• Final Velocity [v]= 20m/s

$\large{\underline{\sf{\blue{SoLution:\rightarrow}}}}$

In how much time will it attain a velocity of 20m/s=>

using this formula,

$\boxed{\sf{a= \dfrac{v-u}{t} } }$

$\sf{\implies 2 = \dfrac{20-6}{t} }$

$\sf{\implies t= \dfrac{14}{2}= 7sec}$

• $\boxed{\bf{\green{ Time = 7sec }}}$

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How much distance will it travel in this time=>

using this formula,

$\boxed{\sf{v^2-u^2 = 2as}}$

$\sf{\implies 20^2 - 6^2 = 2 \times 2 \times s}$

$\sf{\implies s = \dfrac{400-36}{4}}$

$\sf{\implies s= \dfrac{364}{4}}$

• $\boxed{\bf{\green{s= 91m}}}$

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