Question

A car decelerates uniformly from 36 km/h to 18 km/h in 5 s. Calculate the distance traveled.

Answer 1

ɢɪᴠᴇɴ:

$Time \: taken ,(t) = 5 \sec$

$Initial\:velocity ,(u) =18 km/hour$

$u=18×1000 ÷ 60×60s$

$u = 5 m/s$

$Final\:velocity ,(v) =36km/hour$

$v = 36×1000 ÷ 60×60s$

$v =10 m/s$

ᴡᴇ ɴᴇᴇᴅ ᴛᴏ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴀɴᴅ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟᴇᴅ

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

$acceleration \: (a) = (v – u)/t$

sᴜʙsᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇ ɢɪᴠᴇɴ ᴠᴀʟᴜᴇs ɪɴ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇϙᴜᴀᴛɪᴏɴ ᴡᴇ ɢᴇᴛ,

$a = (10 – 5)/5$

$a =5/5$

$a = 1 \: m/ {s}^{2}$

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴅɪsᴛᴀɴᴄᴇ ᴛʀᴀᴠᴇʟʟᴇᴅ ɪs ᴄᴀʟᴄᴜʟᴀᴛᴇᴅ ʙʏ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ

$Distance \: travelled,(S) = u t + (1/2) a × {t}^{2}$

sᴜʙsᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇ ɢɪᴠᴇɴ ᴠᴀʟᴜᴇs ɪɴ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴇϙᴜᴀᴛɪᴏɴ ᴡᴇ ɢᴇᴛ,

$S = 5 × 5 + (1/2) × 1 × 52$

$S = 25 + (1/2) × 25$

$S = 25 + 12.5$

$S = 37.5 m$

ʜᴇɴᴄᴇ,

$acceleration ,(a) =1 m/s²$

$Distance \: travelled ,(S) =37.5 m$