Question

A car starts from rest at velocity 10m/s in 40secs. The driver applies a breakand slows down to 5m/s in 10secs. Find the acceleration in both the cases​

Answer 1

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we Need calculate the acceleration in first case

Initial velocity ,u = 0m/s

Final velocity ,v = 10m/s

Time taken ,t = 40 s

now we need to defined as the rate of change in velocity

A=v-u/t

a denote acceleration

v denote final velocity

u denote initial velocity

t denote time taken

Substitute the value we get

:⟹ a₁ = 10-0/40

:⟹ a₁ = 10/40

:⟹ a₁ = 1/4

:⟹ a₁ = 0.25 m/s²

Hence, the acceleration of the car is 0.25m/s²

Initial velocity ,u = 10m/s

Final velocity ,v = 5m/s

Time taken ,t = 10s

Now, calculating the acceleration in 2nd case .

• a₂ = v-u/t

Substitute the value we get

:⟹ a₂ = 5-10/10

:⟹ a₂ = -5/10

:⟹ a₂ = -0.5 m/s²

Here, negative sign show retardation

Hence, the acceleration in 2nd case is 0.5m/s².

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Answer 2

$\huge \sf {\orange {\underline {\green{\underline {Aɴsᴡᴇʀ}}}}}$

ғɪʀsᴛʟʏ ᴡᴇ ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪɴ 1sᴛ ᴄᴀsᴇ .

ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ,ᴜ = 0ᴍ/s

ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ,ᴠ = 10ᴍ/s

ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ,ᴛ = 40 s

ᴀs ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪs ᴅᴇғɪɴᴇᴅ ᴀs ᴛʜᴇ ʀᴀᴛᴇ ᴏғ ᴄʜᴀɴɢᴇ ɪɴ ᴠᴇʟᴏᴄɪᴛʏ .

• ᴀ = ᴠ-ᴜ/ᴛ

ᴡʜᴇʀᴇ,

• ᴀ ᴅᴇɴᴏᴛᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ

• ᴠ ᴅᴇɴᴏᴛᴇ ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ

• ᴜ ᴅᴇɴᴏᴛᴇ ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ

• ᴛ ᴅᴇɴᴏᴛᴇ ᴛɪᴍᴇ ᴛᴀᴋᴇɴ

sᴜʙsᴛɪᴛᴜᴛᴇ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴡᴇ ɢᴇᴛ

:⟹ ᴀ₁ = 10-0/40

:⟹ ᴀ₁ = 10/40

:⟹ ᴀ₁ = 1/4

:⟹ ᴀ₁ = 0.25 ᴍ/s²

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴄᴀʀ ɪs 0.25ᴍ/s²

_____________________________

• ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ,ᴜ = 10ᴍ/s

• ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ,ᴠ = 5ᴍ/s

• ᴛɪᴍᴇ ᴛᴀᴋᴇɴ ,ᴛ = 10s

ɴᴏᴡ, ᴄᴀʟᴄᴜʟᴀᴛɪɴɢ ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪɴ 2ɴᴅ ᴄᴀsᴇ .

• ᴀ₂ = ᴠ-ᴜ/ᴛ

sᴜʙsᴛɪᴛᴜᴛᴇ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴡᴇ ɢᴇᴛ

:⟹ ᴀ₂ = 5-10/10

:⟹ ᴀ₂ = -5/10

:⟹ ᴀ₂ = -0.5 ᴍ/s²

ʜᴇʀᴇ, ɴᴇɢᴀᴛɪᴠᴇ sɪɢɴ sʜᴏᴡ ʀᴇᴛᴀʀᴅᴀᴛɪᴏɴ

ʜᴇɴᴄᴇ, ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ɪɴ 2ɴᴅ ᴄᴀsᴇ ɪs 0.5ᴍ/s².

Tʜᴀɴᴋs!!