Question

A 30 kg boulder was initially moving at a velocity of 10 m/s, in order to stop it 10 N of
constant retarding force is applied on it. After how long will the boulder stop?​

Answer 1

Answer:

The boulder will stop after 30 s.

Explanation:

Given:

• Mass of boulder (m) = 30 kg
• Initial velocity (u) of the boulder = 10 m/s
• Retarding force = - 10 N

To find:

• After how long will the boulder stop?

Solution:

Final velocity (v) = 0 m/s

We know that,

${\boxed{\sf{Force(F)=Mass(m)\times\: Acceleration (a)}}}$

[ Put values ]

$\implies$ -10 = 30×a

$\implies$ -10 = 30a

$\implies$ a = -⅓

Therefore, aceleration will be - ⅓ m/s².

We know that,

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

Here,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

[ Put values]

$\implies$ 0 = 10 + (-⅓)×t

$\implies$ 0 = 10 - t/3

$\implies$ - t/3 = -10

$\implies$ t = 30

Hence, the boulder will stop after 30 s.

_________________

Some formulas :-

★ v = u + at

★ s = ut + ½ at²

★ v² = u² + 2as

★$\sf{s_n=u+\dfrac{1}{2}a(2n-1)}$

† [ Here, v = Final velocity , u = Initial velocity, a = Acceleration, t = Time, s = Displacement ]

Answer 2

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{Mass \ of \ boulder = 30 \:kg}$

$\:\:\:\:\bullet\:\:\:\sf{Initial\: velocity= 10\:m/s}$

$\:\:\:\:\bullet\:\:\:\sf{Final\: velocity= 0\:m/s}$

$\:\:\:\:\bullet\:\:\:\sf{Retarding \ force = -10N}$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\textsf{After how long will the boulder stop ?}$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

☯ By using F = ma

$\dashrightarrow\:\: \sf{ Force = mass \times acceleration}$

$\dashrightarrow\:\: \sf{-10=30\times a}$

$\dashrightarrow\:\: \sf{-10=30a}$

$\dashrightarrow\:\: \sf{a = -\dfrac{1}{3}m/s^{2}}$

☯ Now, using 1st equation of motion

$\dashrightarrow\:\: \sf{v = u +at}$

$\dashrightarrow\:\: \sf{0= 10-\dfrac{t}{3}}$

$\dashrightarrow\:\: {\boxed{\bf{t = 30\:s}}}$