Question

A force of 4 N acts on a body of mass 2 kg for 4 s. Assuming the body
to be initially at rest, find:
(a) its velocity when the force stops acting
(b) the distance covered in first 10 s after the force starts acting.

Answer 1

Given :-

• Initial velocity, u = 0 m/s (as it is starting from rest)
• Time taken, t = 4 seconds
• Force acting on a body, F = 4 N
• Mass of a body, m = 2 kg

To find :-

• Final velocity, v
• Distance covered, s

According to the question,

a)

➞ Force = Mass × Acceleration

Or,

➞ F = ma

➞ 4 = 2 × a

➞ 4 = 2a

➞ 4 ÷ 2 = a

➞ 2 = a

• So,the acceleration is 2 m/s².

Now,

➞ v = u + at [ First equation of motion ]

Where,

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

➞ Substituting the values,

➞ v = 0 + 2 × 4

➞ v = 0 + 8

➞ v = 8

• So,the final velocity is 8 m/s.

b)

➞ s = ut + ½ at² [ Second equation of motion ]

Where,

• s = Distance
• u = Initial velocity
• a = Acceleration
• t = Time taken

➞ Substituting the values,

➞ s = 0 × 10 + ½ × 2 × 10 × 10

➞ s = 0 + 10 × 10

➞ s = 0 + 100

➞ s = 100

• So, the distance covered in first 10 seconds after the force starts acting is 100 meter.

____________________

Answer 2

Explanation:

$\underline{\bigstar\:\textsf{Given:}}$

• Force (F) = 4 N
• Mass (m) = 2 kg
• Time (t) = 4 s
• Initial velocity (u) = 0 m/s

$\underline{\bigstar\:\textsf{To\:find:}}$

• Final velocity (v) = ?
• Distance covered after 10 second (s) = ?

$\underline{\bigstar\:\textsf{Solution:}}$

(a) We now, $\blue{\sf{F\:=\:ma}}$ and, $\blue{\sf{Acceleration\:=\:(\dfrac{v\:-\:u}{t})}}$

• So, the formula for force (F) = $\sf{m\:\times\:\dfrac{v-u}{t}}$

$\implies\:\sf{4\:=\:2\:\times\:(\dfrac{v\:-\:0}{4})}$

$\implies\:\sf{\dfrac{4}{2}\:=\:\dfrac{v\:-\:0}{4}}$

$\implies\:\sf{2\:\times\:4\:=\:v}$

$\small:\implies\underline{\boxed{\sf\purple{Velocity\:is\:8\:m/s}}}$

(b) Now, we have to find distance after 10 seconds. We know, Newton's 2nd equation of motion i.e, $\blue{\sf{s\:=\:ut\:+\:\dfrac{1}{2}at^2}}$

=> Acceleration = Force/Mass = 4/2 = 2 m/s²

$\implies\:\sf{s\:=\:0\:\times\:10\:+\:\dfrac{1}{2}\:\times\:2\:\times\:(10)^2}$

$\implies$ s = 100 m

$\small:\implies\underline{\boxed{\sf\purple{Distance\:covered\:is\:100\:m}}}$