Question

find the final velocity of a body of mass mass 4kg of a force of 12N acts on it for 5 sec. when it moving with velocity of 10 m/s.​

Answer 1

Answer:

25 m/s

Explanation:

As per the provided information in the given question, we have :

• Mass of the body (m) = 4 kg
• Force acting (F) = 12 N
• Time taken (t) = 5 s
• Initial velocity (u) = 10 m/s

We've been asked to calculate the final velocity of a body.

Here, we'll use the 2nd law of Newton's law of motion. According to the Newton's second law of notion,

$\dashrightarrow \quad \rm {F = ma }$

Acceleration is the rate of change in velocity. So, it can be written as,

$\dashrightarrow \quad \rm {F = m\Bigg ( \dfrac{v-u}{t} \Bigg )}$

Now, we can rearrange the terms after performing multiplication.

$\dashrightarrow \quad \rm {F = \dfrac{m(v-u)}{t} }$

Now, using the distributive property.

$\dashrightarrow \quad \rm {F = \dfrac{mv- mu}{t} }$

Now, substitute the values given in the question.

$\dashrightarrow \quad \rm {12= \dfrac{4v - 4(10)}{5} }$

$\dashrightarrow \quad \rm {12= \dfrac{4v - 40}{5} }$

$\dashrightarrow \quad \rm {12 \times 5= 4v - 40 }$

$\dashrightarrow \quad \rm {60= 4v - 40 }$

$\dashrightarrow \quad \rm {60 + 40= 4v }$

$\dashrightarrow \quad \rm {100= 4v }$

$\dashrightarrow \quad \rm {\cancel{\dfrac{100}{4}} =v }$

$\dashrightarrow \quad \underline{\boxed{ \bf {25 \; m \: s^{-1} = v }}}$

∴ Final velocity of the body is 25 m/s.

$\rule{200}2$

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

Find the final velocity of a body of mass 4 kg if a force of 12N acts on it for 5 sec , when it is moving with velocity of 10 m/s .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

Final velocity of body = 25 m/s

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• Mass of body ( m ) = 4 kg

• Force ( F ) = 12 N

• Time taken ( t ) = 5 s

• Initial velocity ( u ) = 10 m/s

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• Final velocity of body .

$\green{ \large \underline{ \mathbb{\underline{FORMULAS \: USED : }}}}$

$\purple{ \boxed{ \bf a = \frac{v - u}{t} }}$

$\purple{ \boxed{ \bf F = ma}}$

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

$\displaystyle \sf \longrightarrow F = ma \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow F = m \bigg( \frac{v - u}{t} \bigg) \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow F = \frac{m(v - u)}{t} \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow F = \frac{mv - mu}{t} \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow 12 = \frac{4(v) - 4(10)}{5} \\ \\ \displaystyle \sf \longrightarrow 12 \times 5 = 4v - 40 \: \: \\ \\ \displaystyle \sf \longrightarrow 60 = 4v - 40 \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow 4v - 40 = 60 \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow 4v = 60 + 40 \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow 4v = 100 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow v = \frac{100}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \sf \longrightarrow v = 25 \: m {s}^{ - 1} \: \: \: \: \: \: \: \: \: \:$

$\purple{\boxed{\begin{array}{l} \sf{Final \: velocity \: of \: body = 25 \: m {s}^{ - 1}} \end{array}}}$

$\green{ \large \underline{ \mathbb{\underline{KNOW\:MORE: }}}}$

• Acceleration

Acceleration is the rate at which velocity changes with time .

• Initial Velocity

Initial velocity is the velocity of the object before the effect of acceleration .

• Final Velocity

Final velocity is the velocity of the object after the effect of acceleration .

• Force

Force is the push or pull on an object with mass that causes it to change its velocity.

$\Large{\purple{\boxed{\begin{array}{l} \textsf{Equations of motion : } \\ \\ \textsf{v = u + at} \\ \\ \displaystyle\textsf{s = ut + \sf\frac{1}{2}a {t}^{2} } \\ \\ \sf {v}^{2} - {u}^{2} = 2as \end{array}}}}$