Question

A body of mass 1.5kg moving on a horizontal surface with an initial veloclty 6m/sec
comes to rest after 3 secs. If one wants to keep this body moving on same surface
a velocity of 6 m/s. how much force is required.​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Given :

• Mass (m) = 1.5 kg

• Initial Velocity (u) = 6 m/s

• Time (T) = 3 s

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To Find :

• Force required

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Solution :

Final velocity is zero as the mass stops or comes at rest.

We have formula for acceleration,

$\rightarrow {\underline{\boxed{\sf{Acceleration \: = \: \frac{Final \: Velocity \: - \: Initial \: Velocity}{Time}}}}}$

Put Values

⇒a = (0 - 6)/3

⇒a = -6/3

⇒a = -2

∴ Acceleration is -2 m/s²

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Formula for force is :

$\rightarrow {\underline{\boxed{\sf{Force \: = \: Mass \: \times \: Acceleration}}}}$

⇒Force = (1.5)(-2)

⇒Force = -3

∴ Force is 3 N

Here minus sign denotes that force is acting on opposite direction of motion.

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Answer 2

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

From the Question,

• Mass of thr Object,m = 1.5 Kg

• Initial Velocity,u = 0 m/s

• Time taken,t = 3s

$\rule{300}{2}$

To find

Force required to bring the object to rest

Since,

The object is coming to rest,the final velocity of the object would be zero. » v = 0 m/s

From the Relation,

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

Substituting the values,we get :

$\large{ \sf{0 = 6 + 3a}} \\ \\ \large{ \leadsto \: \sf{a = - \frac{6}{3} }} \\ \\ \huge{ \leadsto \: \tt{a = - 2 \: ms {}^{ - 2} }}$

The deceleration of the object is - 2 m/s²

$\rule{300}{2}$

$\rule{300}{2}$

Now,

$\huge{ \boxed{ \boxed{ \sf{f = ma}}}}$

Putting the values,we get :

$\large{ \sf{f = ( - 2)(1.5)}} \\ \\ \huge{ \longrightarrow \: \sf{f = - 3 \: N}}$

The negative sign indicates the action of force towards negative x - axis. In other words,against the direction of motion of the object

The force acting on the object is - 3 N

$\rule{300}{2}$

Note

Direction of velocity in always in direction of motion but direction of acceleration may or may not be in direction of motion

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