Question

A body moving with inital speed 2m/s with uniform acceleration 2m/s for 20 sec if net work done body is 100 joule then find the mass of the body.​

Answer 1

Given:-

• Initial Velocity of body = 2m/s

• Acceleration = 2m/s²

• Time = 20s

• Work Done = 100j

To Find:-

• The mass of the Body

Formulae used:-

• s = ut + ½ × a × t²

• w = F × s

• F = ma

Where,

• s = Displacement
• u = Initial Velocity
• a = Acceleration
• t = Time
• w = work done
• f = Force
• m = mass

Now,

→ s = ut + ½ × a × t²

→ s = 2 × 20 + ½ × 2 × (20)²

→ s = 40 + ½ × 2 × 400

→ s = 40 + 400

→ s = 440m

Hence The Displacement covered by body is 440m.

Therefore,

→ w = f × s

→ 100 = f × 440

→ f = 440/100

→ f = 4.4N.

Hence, The force applied to body is 4.4N

As we find the force applied we can use the equation of Newton's second law i.e,

→ F = ma

→ 4.4 = m × 2

→ m = 4.4/2

→ m = 2kg.

Hence, The mass of the body is 2kg.

Answer 2

GiveN :

• Initial velocity (u) = 2 m/s
• Acceleration (a) = 2 m/s²
• Time (t) = 20 s
• Work Done = 100 J

To FinD :

• Mass of Body

SolutioN :

Use 1st equation of motion :

⇒v = u + at

⇒v = 2 + 2*20

⇒v = 2 + 40

⇒v = 42 m/s

_______________________

Now, use 3rd equation of Motion :

⇒v² - u² = 2as

⇒s = (v² - u²)/2a

⇒s = (42² - 2²)/2*2

⇒s = (1764 - 4)/4

⇒s = 1760/4

⇒s = 440 m

______________________

We know that,

⇒W = Fs

⇒W = ma s

⇒100 = m * 2 * 440

⇒m = 100/880

⇒m = 0.1136 kg