Question

a particle moving with a speed of 20m/s2 accelerated with 5m/s2.Find the distance in 4 seconds​

Answer 1

Given :

• initial velocity = 20 m/s

• acceleration = 5 m / s²

• time taken = 4 seconds

To find :

• Distance travelled

Formula used :

• S = ut + 1/2 at²

where :-

• s = Distance travelled
• u = initial velocity
• a = acceleration
• t = time taken

Solution :

to find distance travelled we will use the following formula :-

⟹ S = ut + 1/2 at²

Now put :-

• u = 20
• a = 5
• t = 4

⟹ S = (20×4) +[( 1/2) × (5) ×( 4²)]

⟹ S = (20×4) +[( 1/2) × (5) × 4 ×4]

⟹ S = 80 + (5× 2 ×4)

⟹ S = 80 + 40

⟹ S = 80 + 40

⟹ S = 120 m

Answer :

Distance travelled = 120 m

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Learn more :-

v= u+at

v= u+atv²-u²= 2as

v= u+atv²-u²= 2ass = ut+1/2at²

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Answer 2

$\huge\sf { \dag Question }$

A particle moving with a speed of 20m/s^2 accelerated with 5m/s^2. Find the distance in 4 seconds.

$\huge\sf { \dag Solution }$

${\underline {\underline {\rm {\red { Given }}}}}$

• $\sf\orange { u ( initial \: velocity ) = 20m/{s}^{2} }$

• $\sf\orange { t( total \: time ) = 4s }$

• $\sf\orange { a( acceleration ) = 5m/{s}^{2} }$

${\underline {\underline {\rm {\red { To \: find }}}}}$

• $\sf { s ( distance \: travelled ) }$

${\underline {\underline {\rm {\red { Calculation }}}}}$

According to the 2nd equation of motion-

${\underline {\underline {\rm {\red { \qquad s = ut + \dfrac{1}{2}a{t}^{2} }}}}}$

Where,

• s = distance travelled
• u = intial velocity
• t = time
• a = acceleration

Substituting values-

$\sf { \qquad \leadsto s = 20 \times 4 + \dfrac{1}{2} \times 5 \times 4 \times 4 }$

$\sf { \qquad \leadsto s = 20 \times \dfrac{1}{2} \times 4 + 5 \times 4 \times 4 }$

$\sf { \qquad \leadsto s = 80 + \dfrac{1}{ \cancel 2} \times 5 \times \cancel { {16}^{ \: \: 8 } } }$

$\sf { \qquad \leadsto s = 80 + 40 }$

$\sf { \qquad \leadsto s = 120m }$

Therefore,the distance in 4 seconds is 120m.

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$\huge\sf { \dag Additional \: Information }$

THREE EQUATIONS OF MOTION-

• ${\underline {\underline {\boxed {\rm {\green { v = u + at }}}}}}$

• ${\underline {\underline {\boxed {\rm {\green { s = ut + \dfrac{1}{2}a{t}^{2} }}}}}}$

• ${\underline {\underline {\boxed {\rm {\green { 2as = {v}^{2} - { u}^{2} }}}}}}$

To solve problems on motion we should always remember that-

• If a body starts from rest or stationary position then u ( initial velocity ) = 0.

• If a body comes to rest or breaks are applied to stop then, v ( final velocity ) = 0.

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