Question

A certain force exerted for 1.2 seconds raises the speed of an object from 1.8 m/s to 4.2 m/s.
Later the same force is applied for 2 seconds. How much does the velocity change in 2 seconds?

Answer 1

$\bigstar$ Answer $\bigstar$

$\checkmark$ Given:

⇒ Time ( t ) = 1.2 seconds

⇒ Initial Velocity ( u ) = 1.8 m/s

⇒ Final Velocity ( v ) = 4.2 m/s

⇒ Change in time ( Δt ) = 2 seconds

$\checkmark$ To Find:

⇒ Change in Velocity ( Δv )

$\checkmark$ Solution:

We know that,

Equation of Motion

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

Since,

The Rate of Change of Velocity with time is know as Acceleration ( a )

So,

Acceleration ( a )

$\pink{\implies \sf a=\dfrac{ \Delta v }{ \Delta t} \ m/s^2}$

$\green{\implies \sf a=\dfrac{v-u}{t} \ m/s^2}$

Given that,

u = 1.8 m/s

v = 4.2 m/s

t = 1.2 sec

Substituting the above values in the Formula

We get,

$\blue{\implies \sf a=\dfrac{4.2-1.8}{1.2} \ m/s^2}$

$\blue{\implies \sf a=\dfrac{2.4}{1.2} \ m/s^2}$

$\orange{\implies \sf a=2 \ m/s^2}$

Therefore,

Acceleration ( a ) = 2 m/s²

According to the Question,

The same force is applied for 2 seconds

We are asked to Find the Change in Velocity in 2 seconds

We know that,

If the Same Force is applied,

It will produce the same Acceleration.

Given that,

The same force is applied for 2 seconds

So, Same same acceleration

Therefore,

Change in Velocity (Δv)

Using the Formula used above,

$\purple {\implies \sf a=\dfrac{ \Delta v }{ \Delta t}}$

So,

$\green{\implies \sf \Delta v =a \times \Delta t}$

Given that,

Δt = 2 sec

And, We found that,

a = 2 m/s²

So,

Substituting the above values in the Formula

We get,

$\pink{\implies \sf \Delta v =2 \times 2 \ m/s}$

$\pink{\implies \sf \Delta v =4 \ m/s}$

$\orange{\boxed{\boxed{\sf \Delta v =4 \ m/s}}}$

Hence,

When same Force is applied,

Change in Velocity ( Δv ) at 2 sec is 4 m/s

Δv = 4 m/s

Answer 2

Answer:

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