Question

A body starting from rest with uniform acceleration if it travels 60 metre in 4 second find the value of acceleration ​

Answer 1

Question :-

A body starting from rest with uniform acceleration . If it travels 60 meters in 4 seconds , what is the value of acceleration ?

Answer :-

Given :-

A body starting from rest with uniform acceleration . If it travels 60 meters in 4 seconds.

Required to find :-

• value of acceleration ?

Concept used :-

• Acceleration is a vector quantity .

• The SI unit of acceleration is m/s² .

• Acceleration is denoted by the letter " a "

Equation used :-

$\large \boxed{ \text{ \pink{s = ut + \frac{1}{2} a {t}^{2} }}}$

Solution :-

Given information :-

A body starting from rest with uniform acceleration . If it travels 60 meters in 4 seconds.

we need to find the value of the acceleration .

So,

From the given infor.ation we can conclude that ;

• Initial velocity of the body = 0 m/s

( Since, the body is at rest )

• Displacement of the body = 60 meters

• Time = 4 seconds

So,

Using the 2nd equation of motion ;

That is ,

$\: \large \boxed{ \text{ \pink{s = ut + \frac{1}{2} a {t}^{2} }}}$

Here,

• s = displacement

• u = initial velocity

• a = acceleration

• t = time

Hence,

Substitute the required values ;

$\rightarrowtail \rm 60 \: = 0 \times 4 + \dfrac{1}{2} \times a \times {4}^{2} \\ \\ \rightarrowtail \rm 60 \: = 0 + \frac{1}{2} \times a \times 4 \times 4 \\ \\ \rightarrowtail \rm 60 \: = 0 + \frac{1}{2} \times a \times 16 \\ \\ \rightarrowtail \rm 60 \: = a \times 8 \\ \\ \rightarrowtail \rm 60 \: = 8a \\ \\ \rightarrowtail \rm \: 8a = 60 \\ \\ \rightarrowtail \rm \: \: a = \frac{60}{8} \\ \\ \implies \rm a = 7.5$

Therefore ,

Acceleration = 7.5 m/s²

Answer 2

Given :

• Initial velocity (u) = 0 m/s
• Distance travelled (s) = 60 m
• Time taken (t) = 4 seconds

_______________________

To Find :

• Value of acceleration (a).

_______________________

Solution :

We know that,

$\large{\implies{\underline{\boxed{\sf{s = ut + \dfrac{1}{2} at^2}}}}} \\ \\ \sf{\dashrightarrow 60 = 0(4) + \dfrac{1}{2} \times a(4)^2} \\ \\ \sf{\dashrightarrow 60 \times 2 = 16a} \\ \\ \sf{\dashrightarrow 120 = 16a} \\ \\ \sf{\dashrightarrow a = \dfrac{120}{16}} \\ \\ \sf{\dashrightarrow a = 7.5} \\ \\ \large{\implies{\underline{\boxed{\sf{a = 7.5 \: ms^{-2}}}}}}$