Question

8.
A body starts from rest and acquires a velocity of 1000cms in 5s. Calculate
the acceleration of the body.​

Answer 1

⭐ Answer ⭐ :

✐ Given :

Initial velocity = 0m/s

Final velocity = 1000 cm/s

Time taken = 5 s

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✑ Required to find :

1. Acceleration of the body

$\rule{400}{4}$

Units Conversion ✍ :

* Before coming to the explanation part .

* However, we have to convert some units to other units .

* In the question it is given ;

Final velocity = 1000cm/s

Here we have to convert the cm/s into m/s .

This is due the fact that ,

The S.I. unit of acceleration is m/s².

Hence,

The formula used to convert the centimeters per second into meters per second .

$\longrightarrow{\boxed{\Rightarrow{\boxed{1\: centimeter\:/\:second\:=\: \frac{1}{100}\: meters\:/\: second}}}}$

Therefore,

$\tt{\longrightarrow{\overbrace{\underbrace{1000\:cm/s = ?\:m/s}}}}$

Hence;

$\implies{\bold{1000\:cm\:/\:s\:=\: \frac {1000}{100}\: meters\:per\: second}}$

$\implies{\bold{1000\:cm\:/\:s\:=\: 10\:meters\:/\: second}}$

Hence,

$\fbox{\color{blue}{\longrightarrow{\boxed{Hence\:1000\:cm\:/\:s\:=\: 10\:meters\:/\: second}}}}$

Similarly

Initial velocity = 0 cm/s = 0 m/s

$\rule{400}{4}$

☛ Explanation :

Knowing about these concepts is important to understand and solve this type of questions .

$\rule{400}{1}$

⚝ What is velocity ?

The displacement of the body per unit of time is know as the velocity of the body .

$\longrightarrow{\textsf{The S.I. unit of velocity is <strong>meter/second</strong><strong> </strong>}}$

As you know that velocity has both magnitude and direction .

So, it is a scalar quantity .

$\rule{400}{1}$

⚝ What is acceleration ?

The change in the velocity per unit of time is know as the acceleration .

The acceleration is represented as ;

$\longrightarrow{\boxed{Acceleration\:=\: \frac {change\:in\:the\: velocity}{change\:in\:time}}}$

$\longrightarrow{\boxed{Acceleration\:=\: \frac {\Delta \:velocity}{\Delta \:time}}}$

Here, This "∆" symbol is known as delta.

Here, delta ( ∆ ) represents change .

$\rule{400}{1}$

☑ Formula :

Let's derive the formula .

$\longrightarrow{\boxed{Acceleration\:=\: \frac {\Delta \:velocity}{\Delta \:time}}}$

∆ velocity refers to Final velocity (b) minus Initial velocity (u) .

similarly,

∆ Time refers to Time only

Hence ;

$\longrightarrow{\boxed{Acceleration\:=\: \frac {Final\:velocity\:-\: Initial\: Velocity}{Time}}}$

This implies ;

$\longrightarrow{\boxed{Hence\:\:Acceleration\:=\: \frac {v\:-\:u}{time}}}$

Hence, using the formula we can find the acceleration .

$\rule{400}{4}$

Solution ☟ :

• Initial velocity ( u ) = 0 m/s
• Final velocity ( v ) = 10 m/s
• Time ( t )= 5 seconds .

Hence,

$\boxed{Acceleration\:=\: \frac {\Delta \:velocity}{\Delta \:time}}$

Substitute the values

we get ;

$\longrightarrow{Acceleration\:=\: \frac {10m/s\:-\:0m/s}{5\: seconds}}$

$\longrightarrow{Acceleration\:=\: \frac {10m/s}{5\: seconds}}$

$\implies{Acceleration\:=\: 2 meter/{second}^{2}}$

Therefore ,

$\rightarrow{\boxed{\Large{Acceleration\:is\:2\:meter/{second}^{2}}}}$

✅ Hence Solved . ☚

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Answer 2

Answer:

⭐ Answer ⭐ :

✐ Given :

Initial velocity = 0m/s

Final velocity = 1000 cm/s

Time taken = 5 s

\rule{400}{4}

✑ Required to find :

Acceleration of the body

\rule{400}{4}

Units Conversion ✍ :

* Before coming to the explanation part .

* However, we have to convert some units to other units .

* In the question it is given ;

Final velocity = 1000cm/s

Here we have to convert the cm/s into m/s .

This is due the fact that ,

The S.I. unit of acceleration is m/s².

Hence,

The formula used to convert the centimeters per second into meters per second .

\longrightarrow{\boxed{\Rightarrow{\boxed{1\: centimeter\:/\:second\:=\: \frac{1}{100}\: meters\:/\: second}}}}⟶

⇒

1centimeter/second=

100

1

meters/second

Therefore,

\tt{\longrightarrow{\overbrace{\underbrace{1000\:cm/s = ?\:m/s}}}}⟶

1000cm/s=?m/s

Hence;

\implies{\bold{1000\:cm\:/\:s\:=\: \frac {1000}{100}\: meters\:per\: second}}⟹1000cm/s=

100

1000

meterspersecond

\implies{\bold{1000\:cm\:/\:s\:=\: 10\:meters\:/\: second}}⟹1000cm/s=10meters/second

Hence,

\fbox{\color{blue}{\longrightarrow{\boxed{Hence\:1000\:cm\:/\:s\:=\: 10\:meters\:/\: second}}}}

\longrightarrow

Hence1000cm/s=10meters/second

Similarly

Initial velocity = 0 cm/s = 0 m/s

\rule{400}{4}

☛ Explanation :

Knowing about these concepts is important to understand and solve this type of questions .

\rule{400}{1}

⚝ What is velocity ?

The displacement of the body per unit of time is know as the velocity of the body .

\longrightarrow{\textsf{The S.I. unit of velocity is < strong > meter/second < /strong > < strong > < /strong > }}⟶The S.I. unit of velocity is < strong > meter/second < /strong > < strong > < /strong >

As you know that velocity has both magnitude and direction .

So, it is a scalar quantity .

\rule{400}{1}

⚝ What is acceleration ?

The change in the velocity per unit of time is know as the acceleration .

The acceleration is represented as ;

\longrightarrow{\boxed{Acceleration\:=\: \frac {change\:in\:the\: velocity}{change\:in\:time}}}⟶

Acceleration=

changeintime

changeinthevelocity

\longrightarrow{\boxed{Acceleration\:=\: \frac {\Delta \:velocity}{\Delta \:time}}}⟶

Acceleration=

Δtime

Δvelocity

Here, This "∆" symbol is known as delta.

Here, delta ( ∆ ) represents change .

\rule{400}{1}

☑ Formula :

Let's derive the formula .

\longrightarrow{\boxed{Acceleration\:=\: \frac {\Delta \:velocity}{\Delta \:time}}}⟶

Acceleration=

Δtime

Δvelocity

∆ velocity refers to Final velocity (b) minus Initial velocity (u) .

similarly,

∆ Time refers to Time only

Hence ;

\longrightarrow{\boxed{Acceleration\:=\: \frac {Final\:velocity\:-\: Initial\: Velocity}{Time}}}⟶

Acceleration=

Time

Finalvelocity−InitialVelocity

This implies ;

\longrightarrow{\boxed{Hence\:\:Acceleration\:=\: \frac {v\:-\:u}{time}}}⟶

HenceAcceleration=

time

v−u

Hence, using the formula we can find the acceleration .

\rule{400}{4}

Solution ☟ :

Initial velocity ( u ) = 0 m/s

Final velocity ( v ) = 10 m/s

Time ( t )= 5 seconds .

Hence,

\boxed{Acceleration\:=\: \frac {\Delta \:velocity}{\Delta \:time}}

Acceleration=

Δtime

Δvelocity

Substitute the values

we get ;

\longrightarrow{Acceleration\:=\: \frac {10m/s\:-\:0m/s}{5\: seconds}}⟶Acceleration=

5seconds

10m/s−0m/s

\longrightarrow{Acceleration\:=\: \frac {10m/s}{5\: seconds}}⟶Acceleration=

5seconds

10m/s

\implies{Acceleration\:=\: 2 meter/{second}^{2}}⟹Acceleration=2meter/second

2

Therefore ,

\rightarrow{\boxed{\Large{Acceleration\:is\:2\:meter/{second}^{2}}}}→

Accelerationis2meter/second

2

✅ Hence Solved . ☚

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