Question

Problem 2: A constant force is applied to a body of mass 100 g initially at
rest. If the body acquires a velocity of 10 m/s in 5 seconds, determine the force.​

Answer 1

Solution:

Given that:

• A constant force is applied to a body of mass 100 g initially at rest.
• The body acquires a velocity of 10 m/s in 5 seconds.

Abbreviations:

• u = Initial velocity
• v = Final velocity
• t = Time taken to acquire velocity
• a = Acceleration
• m = Mass
• F = Force

We have:

• u = 0 m/s
• v = 10 m/s
• t = 5 seconds

We know that:

→ a = (v - u)/t

→ a = (10 - 0)/5

→ a = 10/5

→ a = 2

⁂ Acceleration = 2 m/s²

Now we have:

• m = 100 g = 100/1000 = 0.1 kg
• a = 2 m/s²

We know that:

→ F = ma

→ F = 0.1 × 2

→ F = 0.2

⁂ Force = 0.2 N

Answer 2

Answer:

Given :-

• A constant force is applied to a body of mass 100 g initially at rest.
• The body acquires a velocity of 10 m/s in 5 seconds.

To Find :-

• What is the force.

Formula Used :-

$\clubsuit$ Acceleration Formula :

$\longmapsto \sf\boxed{\bold{\pink{Acceleration =\: \dfrac{Final\: Velocity\: -\: Initial\: Velocity}{Time}}}}$

$\clubsuit$ Force Formula :

$\longmapsto \sf\boxed{\bold{\pink{Force =\: Mass \times Acceleration}}}$

Solution :-

First, we have to find the acceleration :

Given :

• Final Velocity (v) = 10 m/s
• Initial Velocity (u) = 0 m/s
• Time = 5 seconds

According to the question by using the formula we get,

$\implies \sf Acceleration =\: \dfrac{10 - 0}{5}$

$\implies \sf Acceleration =\: \dfrac{\cancel{10}}{\cancel{5}}$

$\implies \sf Acceleration =\: \dfrac{2}{1}$

$\implies \sf\bold{\green{Acceleration =\: 2\: m/s^2}}$

Hence, the acceleration is 2 m/s².

Now, we have to find force :

At first we have to convert the mass into kg :

$\implies \sf Mass =\: 100\: g$

$\implies \sf Mass =\: \dfrac{100}{1000}\: kg\: \bigg\lgroup \sf\bold{\purple{1\: g =\: \dfrac{1}{1000}}}\bigg \rgroup$

$\implies \sf\bold{\green{Mass =\: 0.1\: kg}}$

Given :

• Mass = 0.1 kg
• Acceleration = 2 m/s²

According to the question by using the formula we get,

$\dashrightarrow \sf Force =\: 0.1 \times 2$

$\dashrightarrow \sf Force =\: \dfrac{1}{10} \times 2$

$\dashrightarrow \sf Force =\: \dfrac{2}{10}$

$\dashrightarrow \sf\bold{\red{Force =\: 0.2\: N}}$

$\therefore$ The force is 0.2 N .