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 i

2 thoughts on “Problem 2: A constant force is applied to a body of mass 100 g initially at<br />rest. If the body acquires a velocity of 10 m/s i”

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

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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 :-

   [tex]\clubsuit[/tex] Acceleration Formula :

   [tex]\longmapsto \sf\boxed{\bold{\pink{Acceleration =\: \dfrac{Final\: Velocity\: -\: Initial\: Velocity}{Time}}}}\\[/tex]

   [tex]\clubsuit[/tex] Force Formula :

   [tex]\longmapsto \sf\boxed{\bold{\pink{Force =\: Mass \times Acceleration}}}\\[/tex]

   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,

   [tex]\implies \sf Acceleration =\: \dfrac{10 – 0}{5}[/tex]

   [tex]\implies \sf Acceleration =\: \dfrac{\cancel{10}}{\cancel{5}}[/tex]

   [tex]\implies \sf Acceleration =\: \dfrac{2}{1}[/tex]

   [tex]\implies \sf\bold{\green{Acceleration =\: 2\: m/s^2}}[/tex]

   Hence, the acceleration is 2 m/s².

   Now, we have to find force :

   At first we have to convert the mass into kg :

   [tex]\implies \sf Mass =\: 100\: g[/tex]

   [tex]\implies \sf Mass =\: \dfrac{100}{1000}\: kg\: \bigg\lgroup \sf\bold{\purple{1\: g =\: \dfrac{1}{1000}}}\bigg \rgroup\\[/tex]

   [tex]\implies \sf\bold{\green{Mass =\: 0.1\: kg}}[/tex]

   Given :

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

   According to the question by using the formula we get,

   [tex]\dashrightarrow \sf Force =\: 0.1 \times 2[/tex]

   [tex]\dashrightarrow \sf Force =\: \dfrac{1}{10} \times 2[/tex]

   [tex]\dashrightarrow \sf Force =\: \dfrac{2}{10}[/tex]

   [tex]\dashrightarrow \sf\bold{\red{Force =\: 0.2\: N}}[/tex]

   [tex]\therefore[/tex] The force is 0.2 N .

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