Question

A body starting from rest has an acceleration of 20 metre second -2 the distance travelled by it in the 6th second will be

Answer 1

$\begin{lgathered}\boxed{\pink{\mathfrak{\huge{Given}}} \begin{cases} \sf Initial Velocity, u = 0m/s \\ \\ \\ \sf Acceleration,a = 20 {m/s}^{2} \\ \\ \\ \sf Time,t = 6sec \end{cases}} \end{lgathered}$

$\begin{lgathered}\boxed{\purple{\mathfrak{\huge{Find}}} \begin{cases} \\ \\ \sf Distance \: Travelled \: by \: body \\ \\ \\ \end{cases}} \end{lgathered}$

$\boxed{\orange{\mathfrak{\huge{Solution}}}}$

we, know that

$\large{\boxed{\sf s_{n} = u + \dfrac{1}{2}a(2n - 1)}}$

where,

• n = 6sec
• u = 0m/s
• a = 20m/s²

So,

$\dashrightarrow\sf s_{n} = u + \dfrac{1}{2}a(2n - 1) \\ \\ \\ \dashrightarrow\sf s_{6} = 0 + \dfrac{1}{2}(20) \big\lgroup{2(6) - 1} \big\rgroup \\ \\ \\ \dashrightarrow\sf s_{6} = 10 \big\lgroup{2(6) - 1} \big\rgroup \\ \\ \\ \dashrightarrow\sf s_{6} = 10 \big\lgroup{12 - 1} \big\rgroup \\ \\ \\ \dashrightarrow\sf s_{6} = 10 \big\lgroup{11} \big\rgroup \\ \\ \\ \dashrightarrow\sf s_{6} =110m$

Hence, Distance Travelled by the body in 6sec is = 110m

Answer 2

ɢɪᴠᴇɴ:-

Initial velocity (u) = 0 m/s (Starts from rest)

Accelration (a) = 20 m/s²

Time (n) = 6 sec

ᴛᴏ ꜰɪɴᴅ:-

• Distance travelled

ꜱᴏʟᴜᴛɪᴏɴ:-

✰Distance covered by moving body in nth second of journey is given by,

$\bigstar\:\underline{\boxed{\bf{\pink{s_n=u+\dfrac{1}{2}\times a(2n-1)}}}}$

• $\tt s_n$denotes distance covered in nth second
• u denotes initial velocity
• a denotes acceleration
• n denotes no. of second

$\begin{lgathered}\rm \implies s_{n^{th}} = 0 + \frac{1}{2} \times 20(2 \times 6 - 1) \\ \\ \tt :\implies s_{n^{th}} =10(12 - 1) \\ \\ \tt :\implies s_{n^{th}} =10 \times 11 \\ \\ \tt :\implies s_{n^{th}} =110 \: m\end{lgathered}$

Hence, Distance Travelled by the body in 6sec is $\overbrace{ \underbrace{ \boxed{\red{110m}}}}$

━━━━━━━━━━━━━━━━━━━━━━