Question

Starting from rest a body is moving with uniform acceleration of 2 m/s^2. find its displacement in 5th seconds.

Answer 1

Given :-

Starting from rest a body is moving with a uniform acceleration of 2 m/s²

Required to find :-

• Displacement in the 5 seconds

Concept used :-

• Displacement is the shortest path between any two given points .

• Displacement is a vector quantity .

• The SI unit of displacement is meter .

• Displacement has both magnitude and direction .

Equations used :-

➾ v = u + at

➾ v² - u² = 2as

Solution :-

Given information :-

Starting from rest a body is moving with a uniform acceleration of 2 m/s²

we need to find the displacement after 5 seconds

So,

From the given information we can conclude that ;

Since,

The body is at rest

• Initial velocity of the body ( u ) = 0 m/s

similarly,

The body started moving with uniform acceleration of 2 m/s² from rest position

So,

• Acceleration of the body ( a ) = 2 m/s²

Since, we need to find the displacement in 5 seconds

Hence,

• Time = 5 seconds

Using the 1st equation of motion

Hence,

➦ v = 0 + ( 2 m/s² )( 5 s )

➦ v = 0 + 10 m/s

➦ v = 10 m/s

So,

• Final velocity ( v ) = 10 m/s

Now,

Using the 3rd Equation of motion

v² - u² = 2as

So,

Substitute the required values ;

➜ ( 10 m/s )² - ( 0 m/s )² = 2 x 2 m/s² x s

➜ 100 m²/s² - 0 m/s² = 4 m/s² x s

➜ 100 m²/s² = 4 m/s² x s

➜ 4 m/s x s = 100 m²/s²

➜ s = 100 m/s²/4 m²/s²

➜ s = 25 meters

Since , s = displacement

So,

Displacement of the body after 5 seconds = 25 meters

Answer 2

→ Given ←

Starting from rest a body is moving with uniform acceleration of 2 m/s².

• Initial velocity, u = 0 m/s
• Acceleration, a = 2 m/s²

$\rule{180}{2.5}$

→ To Find ←

The displacement is the 5th second(t = 5 s).

$\rule{180}{2.5}$

→ Solution ←

We know,

$\boxed{\sf{\bigstar\ \color{red}{v=u+at}}}$

Putting the values :-

$\displaystyle{\rm{\dashrightarrow v=0+2(5)}}\\\\\displaystyle{\rm{\dashrightarrow v=10\ m/s}}$

$\rule{90}2$

We also know that,

$\boxed{\sf{\bigstar\ \color{red}{v^2=u^2+2as}}}$

Putting the values :-

$\displaystyle{\rm{\dashrightarrow (10)^2=(0)^2+2\times2\times s}}\\\\\displaystyle{\rm{\dashrightarrow 100=0+4s}}\\\\\displaystyle{\rm{\dashrightarrow 4s=100}}\\\\\displaystyle{\rm{\dashrightarrow s=\frac{100}{4} }}\\\\\large\boxed{\boxed{\displaystyle{\rm \color{lime}{{\dashrightarrow s=25\ m}}}}}$

Therefore, the body has a displacement of 25 m in the 5th second.