Question

A body starts from rest and moves with a uniform acceleration of 2 m s/ 2 - until it travels a distance of 625 m. Find its velocity.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Final\:velocity=50\:m/s}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Acceleration(a) = 2 \: m/s^{2} \\ \\ \tt: \implies Distance(s) = 625\: m \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies Final\:velocity(v) = ?$

• According to given question :

$\tt \circ \: Initial \: speed = 0\: m/s \\ \\ \tt \circ \: Distance= 625 \\\\ \tt\circ\:Acceleration=2\:m/s^{2} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies v^{2} = u^{2} + 2as \\ \\ \tt: \implies v^{2} =0^{2}+2\times 2\times 625 \\ \\ \tt: \implies v^{2} =4\times 625 \\ \\ \tt: \implies v^{2}=2500 \\ \\ \tt: \implies v= \sqrt{2500} \\ \\ \green{\tt: \implies v = 50\:m/s } \\ \\ \green{\tt \therefore Velocity \: after\:travelling\:625\:m \: is \: 50\: {m/s} } \\ \\ \blue{ \bold{Some \: related \: formula}} \\ \orange{ \tt \circ \: v = {u} +at} \\ \\ \orange{ \tt \circ \: s = ut+ \frac{1}{2}a {t}^{2} }$

Answer 2

Aɴꜱᴡᴇʀ

v = 50 m/s

_________________

Gɪᴠᴇɴ

$\sf{} \bigstar \:initial \: velocity \: (u) = 0 \: m/s \\ \\ \sf{}\bigstar distance = 625 \: m \\ \\ \sf \bigstar acceleration = 2m/ {s}^{2}$

_________________

ᴛᴏ ꜰɪɴᴅ

The velocity of the body

_________________

Sᴛᴇᴘꜱ

As we already know the initial velocity of the body, the distance travelled and the acceleration of the body , the formula that fits the given data is obviously

$\large \orange{ \tt{} {v}^{2} - {u}^{2} = 2as }$

Where,

• v = is the final velocity

• u is the initial velocity

• a is the accelerataion

• and s is the distance

Calculation:-

$\tt{} \leadsto{} {v}^{2} = {u}^{2} + 2as \\ \\ \tt{} \leadsto {v}^{2} = {0}^{2} + 2(2)(625) \\ \\ \tt{} \leadsto {v}^{2} = 2500 \\ \\ \tt{} \leadsto v = \sqrt{2500} \\ \\ \large\tt{} \purple{ \dashrightarrow{}v = 50 \: m/s}$

_________________

Some important formulas :-

• v = u+at

• $\sf{}s =ut +\frac{1}{2} a{t}^{2}$