Question

a body travels 35m during the 6th second and 45m during the 8th second. find the initial velocity and acceleration​

Answer 1

Answer:

5m/s²,7.5m/s

Explanation:

displacement during any second St=u+at-½a

35=u+6a-½a

45=u+8a-½a

subtracting 1st equation from the second,

a=5m/s²

substituting to first equation,

u=7.5m/s

Answer 2

$\Large\bf{\color{indigo}GiVeN,}$

• A body travels 35 m during the 6th second.

• That body travels 45 m during the 8th second.

$\bf\blue{We\:know\:that,}$

☆ Distance travelled by uniformly accelerated body in nᵗʰ seconds is given by,

$\red\bigstar\:\:{\green{\boxed{\bf{\color{peru}S_n\:=\:u\:+\:\dfrac{1}{2}\:a\:(2n\:-\:1)\:}}}}$

$\bf\pink{Where,}$

• u is the initial velocity.

• a is the acceleration of the body.

ƇƛƧЄ - 1 :-

• n = 6 (6th second)

• S₆ = 35 m

$:\implies\:\:\bf{35\:=\:u\:+\:\dfrac{1}{2}\:a\:(2\times{6}\:-\:1)\:}$

$:\implies\:\:\bf{35\:=\:u\:+\:\dfrac{1}{2}\:a\:(12\:-\:1)\:}$

$:\implies\:\:\bf{35\:=\:u\:+\:\dfrac{1}{2}\:a\times{11}\:}$

$:\implies\:\:\bf{\color{olive}35\:=\:u\:+\:\dfrac{11}{2}\:a\:}--(i)$

ƇƛƧЄ - 2 :-

• n = 8 (8th second)

• S₈ = 45 m

$:\implies\:\:\bf{45\:=\:u\:+\:\dfrac{1}{2}\:a\:(2\times{8}\:-\:1)\:}$

$:\implies\:\:\bf{45\:=\:u\:+\:\dfrac{1}{2}\:a\:(16\:-\:1)\:}$

$:\implies\:\:\bf{45\:=\:u\:+\:\dfrac{1}{2}\:a\times{15}\:}$

$:\implies\:\:\bf\red{45\:=\:u\:+\:\dfrac{15}{2}\:a\:}--(ii)$

$\bf\purple{Subtract\:equation(1)\:from\:(2),}$

$\longrightarrow\:\:\bf{45\:-\:35\:=\:(u\:-\:u)\:+\:\Big(\dfrac{15}{2}\:a\:-\:\dfrac{11}{2}\:a\Big)}$

$\longrightarrow\:\:\bf{10\:=\:0\:+\:\Big(\dfrac{15a\:-\:11a}{2}\Big)}$

$\longrightarrow\:\:\bf{10\:=\:\dfrac{4a}{2}}$

$\longrightarrow\:\:\bf{10\:=\:2a}$

$\longrightarrow\:\:\bf{a\:=\:\dfrac{10}{2}}$

$\longrightarrow\:\:\bf\orange{a\:=\:5\:m/s^2}$

✒ Putting the value of a in the equation(i),

$\longrightarrow\:\:\bf{35\:=\:u\:+\:\dfrac{11}{2}\times{5}\:}$

$\longrightarrow\:\:\bf{35\:=\:u\:+\:\dfrac{55}{2}\:}$

$\longrightarrow\:\:\bf{u\:=\:35\:-\:\dfrac{55}{2}\:}$

$\longrightarrow\:\:\bf{u\:=\:\dfrac{70\:-\:55}{2}\:}$

$\longrightarrow\:\:\bf{u\:=\:\dfrac{15}{2}\:}$

$\longrightarrow\:\:\bf\green{u\:=\:7.5\:m\:}$

$\Large\bold\therefore$ The initial velocity is 7.5 m & acceleration is 5 m/s².