Question

A body moving with an initial velocity of 3m/s starts deccelerating at the rate of 2m/s^2.Find the distance travelled after 4 seconds.​

Answer 1

Question : -

A body moving with an initial velocity of 3m/s starts accelerating at the rate of 2m/s² . Find the distance travelled after 4 seconds.

: - ANSWER - :

Given : -

A body moving with an initial velocity of 3 m/s starts decelerating at the rate of 2 m/s².

Required to find : -

Find the distance travelled after 4 seconds ?

Equations used : -

• 1. v = u + at

• 2. v² - u² = 2as

Here,

v = Final velocity

u = Initial velocity

a = acceleration

t = time taken

s = displacement

Solution : -

A body moving with an initial velocity of 3 m/s starts decelerating at the rate of 2 m/s².

we need to find the distance travelled in 4 seconds ?

From the given information we can conclude that ;

• Initial velocity of the body ( u ) = 3 m/s

• Decelerating ( a ) = 2 m/s²

• Time ( t ) = 4 seconds

Now,

Let's find the final velocity of the body .

Using the equation of motion ;

i.e. v = u + at

➜ v = 3 + 2 x 4

➜ v = 3 + 8

➜ v = 11 m/s

Hence,

Final velocity of the body ( v ) = 11 m/s

Now,

Let's find the displacement of the body

Using the equation of motion ;

i.e. v² - u² = 2as

➜ ( 11 )² - ( 3 )² = 2 x 2 x s

➜ 121 - 9 = 4 x s

➜ 112 = 4 x s

➜ 112 = 4s

➜ 4s = 112

➜ s = 112/4

➜ s = 28 meters

Hence,

Displacement of the body ( s ) = 28 meters

Since,

In some cases , we can take displacement in the terms of distance .

Therefore,

Distance travelled by the body in 4 seconds = 28 meters

-: Additional Information :-

Question : -

What relationship does the three equations of motion gives us ?

Answer : -

The 1st equation of motion gives us the relationship between the final velocity and time

The 2nd equation of motion gives us the relationship between the displacement and time

The 3rd equation of motion gives us the relationship between the final velocity and displacement .

Question :-

What is decelerating / deceleration ?

Answer : -

Negative acceleration is termed as Deceleration .

The SI unit of acceleration is m/s² .

Question : -

What is Acceleration ?

Answer : -

Acceleration is the change in the velocity per unit time .

Represented as.

Acceleration = ∆v/∆t

Answer 2

Answer

distance travelled after 4 seconds is 28 m

Given ( Correction )

A body moving with an initial velocity of 3 m/s starts accelerating at the rate of 2 m/s²

To Find

Distance travelled after 4 seconds

Concept Used

As the acceleration is constant , so we can apply equations of kinematics

Equation's of motion

→ v = u + at

→ s = ut + ¹/₂ at²

→ v² - u² = 2as

Solution

Initial velocity , u = 3 m/s

acceleration , a =  2 m/s²

Time , t = 4 s

Distance , s = ? m

Apply 1st equation of motion ,

⇒ v = u + at

⇒ v = 3 + (2)(4)

⇒ v = 3 + 8

⇒ v = 11 m/s

So , Final velocity , v = 11 m/s

________________________

Apply 3rd equation of motion ,

⇒ v² - u² = 2as

⇒ (11)² - (3)² = 2(2)s

⇒ 121 - 9 = 4s

⇒ 112 = 4s

⇒ 4s = 112

⇒ s = 28 m

So , Distance , s = 28 m