Question

A body at rest acquired a velocity 100 ms^-1 within 50 m with uniform acceleration find the acceleration.

Answer 1

Given:

Initial velocity of body, u= 0 m/s

(Since it starts from rest)

Final velocity of body, v= 100 m/s

Displacement of body, s= 50 m

To Find:

Acceleration of body

Solution:

We know that,

• According to third equation of motion for constant acceleration

$\pink{\boxed{\bf{v^{2}-u^{2}=2as}}}$

where

v is final velocity of body

u is initial velocity of body

a is acceleration of body

s is displacement of body

$\rule{190}{1}$

Let the acceleration of given body be 'a'

So, on applying third equation of motion of given body, we get

$\longrightarrow\rm{v^{2}-u^{2}=2as}$

$\longrightarrow\rm{(100)^{2}-(0)^{2}=2a(50)}$

$\longrightarrow\rm{10000=100a}$

$\longrightarrow\rm{100a=10000}$

$\longrightarrow\rm{a=\dfrac{\cancel{10000}}{\cancel{100}}}$

$\longrightarrow\rm\green{a=100\:m/s^{2}}$

Hence, the acceleration of given body is 100 m/s².

Answer 2

$\rule{200}4$

$\huge\tt{GIVEN:}$

• A body at rest acquired velocity of 100 ms-¹ within 50 m with an uniform acceleration.

$\rule{200}2$

$\huge\tt{TO~FIND:}$

• The acceleration of the body.

$\rule{200}2$

$\huge\tt{CONCEPT~USED:}$

According to the equation of motion for constant acceleration,

${\underline{\fbox{\fbox{\mathbb{\blue{V^2~-~U^2~=~2as}}}}}}$

Where, v = final velocity, u = initial velocity , a = acceleration , s = displacement.

$\rule{200}2$

$\huge\tt{SOLUTION:}$

Let us assume that the acceleration of the body is a.

So, if we apply the equation, we get,

↪v² - u² = 2as

↪(100)² - (0)² = 2a(50)

↪10000 = 100a

↪10000/100 = a

↪100 m/s² = a

$\huge{\fbox{\fbox{\fbox{\tt{\red{100~m~/~s^2}}}}}}$

$\rule{200}4$