Question

If a body having mass 40kg started moving initially with rest and it takes a velocity of 20m/sec in time 4 seconds. Find the value of force​

Answer 1

Answer :

• Force exerted by the body, F = 200 N.

Explanation :

Given :

• Mass of the body, m = 40 kg
• Final velocity of the body, v = 20 m/s
• Initial velocity of the body, u = 0

[Since the body is starting from rest the initial velocity of the body will be taken as zero]

• Time taken to change the velocity, t = 4 s

To find :

• Force exerted by the body, F = ?

Knowledge required :

• First equation of motion :

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = u + at⠀

[Where : v = Final velocity of the body, u = Initial velocity of the body, a = Acceleration due to gravity, t = Time Taken]

• Formula for force exerted by a body :

⠀⠀⠀⠀⠀⠀⠀⠀⠀F = ma⠀

[Where : F = Force exerted by the body, m = mass of the body, a = Acceleration due to gravity]

Solution :

To find the acceleration produced by the body :

⠀⠀By using the first equation of motion and substituting the values in it, we get :

⠀⠀=> v = u + at

⠀⠀=> 20 = 0 + a(4)

⠀⠀=> 20 = 4a

⠀⠀=> 20/4 = a

⠀⠀=> 5 = a

⠀⠀⠀⠀∴ a = 5 m/s²

Hence the acceleration produced by the body is 5 m/s²

To find the force exerted by the body :

⠀⠀By using the formula for force exerted by a body and substituting the values in it, we get :

⠀⠀=> F = ma

⠀⠀=> F = 40 × 5

⠀⠀=> F = 200

⠀⠀⠀⠀∴ F = 200 N

Hence the force exerted by the body is 200 N.

Answer 2

$\large{\boxed{\underline{\sf{Question \: is \: given}}}}$

If a body having mass 40kg started moving initially with rest and it takes velocity of 20m/sec in time 4 seconds. Find the value of force.

$\large{\boxed{\underline{\sf{Answer}}}}$

$\large{\boxed{\underbrace{\sf{Given \: that}}}}$

✠ Mass of body = 40 kilograms.

✠ Initial velocity = 0 m/s

✠ Final velocity = 20 m/s

✠ Time = 4 seconds

$\large{\boxed{\sf{Why \: initial \: velocity \: is \: 0m/s}}}$

✠ The initial velocity will be 0 because at that time the body is at a rest. And when a body is at rest then the velocity becomes 0 by itself.

$\large{\boxed{\underbrace{\sf{To \: find}}}}$

✠ Value of force exerted.

$\large{\boxed{\underbrace{\sf{Solution}}}}$

✠ Value of force = 200N

$\large{\boxed{\underbrace{\sf{Understanding \: the \: concept}}}}$

✠ This question says that there is a body of mass 40 kg started moving at a final velocity of 20 m/s and it's initial velocity be 0 m/s because that time this body is at a rest. Afterwards this question ask us to find the force exerted by the body. And the time is also given as 4 seconds.

$\large{\boxed{\underbrace{\sf{Procedure}}}}$

✠ To solve this question 1stly we have to use the Newton's first law of motion formula afterthat putting the values we get the acceleration produced by the body. Now finding the force exerted we have to use the formula of force we have to use it's formula and putting the values we get our final result as 200N

$\large{\boxed{\underbrace{\sf{We \: also \: write \: these \: as}}}}$

✠ Final velocity as v.

✠ Initial velocity as u.

✠ Mass as m.

✠Acceleration as a

$\large{\boxed{\underbrace{\sf{Using \: concepts}}}}$

✠ Newton's first equation of motion.

✠ Force exerted by the body

$\large{\boxed{\underbrace{\sf{Using \: formulas}}}}$

✠ 1st equation of motion ↝ v = u + at

✠ Force exerted by body ↝ F = ma

$\large{\boxed{\underbrace{\sf{Full \: solution}}}}$

$\large{\boxed{\bf{Acceleration \: produced \: by \: the \: body}}}$

Using formula of 1st equation of motion and putting the values we get the following results.

➨ v = u + at

➨ 20 = 0 + a(4)

➨ 20 = 0 +a4

➨ 20-0 = a4

➨ 20 = a4

➨ 20/4 = a

➨ 5 = a

➨ a = 5 m/s²

$\large{\boxed{\bf{Force \: exerted \: by \: the \: body}}}$

Using formula of finding force and putting the values we get the following results.

➨ F = ma

➨ F = 40(5)

➨ F = 200

➨ F = 200 N