Question

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1. A body of mass 500 g, initially at rest, is acted upon
by a force which causes it to move a distance of 4
m in 2 s. Calculate the force applied.​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Mass of body (m) = 500g or 0.5kg
• Initially body is at rest (u) = 0
• When force is applied it moves by distance (s) = 4m in time (t) =2s

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Force applied ( F )

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❏ Velocity

$\color{violet}\bullet\underline{\boxed{\sf Velocity=\dfrac{s}{t}}}$

v = finial Velocity of body

s = distance

t = time

$\implies{\sf v =\dfrac{4}{2}}$

$\color{orange}\implies{\sf v = 2m/s}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

❏ Acceleration

From Newton's First Law Of Motion

$\color{violet}\bullet\underline{\boxed{\sf v=u+at}}$

v = final velocity of body

u = Initial velocity of body

a = acceleration

t = time

$\implies{\sf 2=0+a×2 }$

$\color{orange}\implies{\sf a=1\:m/s^2}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

From Newton's Second Law

$\Large\color{violet}\bullet\underline{\boxed{\sf F=ma}}$

F = force applied

m = mass of body

a = acceleration

$\implies{\sf F=0.5×1 }$

$\color{red}\implies{\sf F=0.5N}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Force applied to the body is $\color{red}{\sf 0.5N}$

Answer 2

Answer:

• The Force (F) Applied on the body is 1 N.

Given:

1. Mass of the body (M) = 500 g = 0.5 Kg
2. Distance covered (S) = 4 m
3. Time taken (t) = 2 sec.
4. Initial velocity (u) = 0 m/s.

Explanation:

$\rule{300}{1.5}$

From second Kinematic equation we know,

⇒ S = u t + 1 / 2 a t²

Where,

• S Denotes Distance travelled.
• u Denotes Initial velocity.
• t Denotes Time taken.
• a Denotes Acceleration.

Now,

⇒ S = u t + 1 / 2 a t²

Substituting the values,

⇒ 4 = 0 × 2 + 1 / 2 × a × (2)²

⇒ 4 = 0 + 1 / 2 × a × 4

⇒ 4 = 1 / 2 × a × 4

⇒ 4 = a × 2

⇒ a = 4 / 2

⇒ a = 2

⇒ a = 2 m/s²

∴ We got the acceleration.

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From Newton's Second law

⇒ F = M a

Where,

• F Denotes Force.
• M Denotes Mass.
• a Denotes acceleration.

Now,

⇒ F = M a

Substituting the values,

⇒ F = 0.5 Kg × 2 m/s²

⇒ F = 0.5 × 0.2

⇒ F = 1

⇒ F = 1 N.

∴ The Force (F) Applied on the body is 1 N.

$\rule{300}{1.5}$