Question

A car travelling at 36 km/hr speeds upto 54 km/hr in 5 seconds. What is its acceleration? If the same car stops in 20 s, what is the retardation?

Answer 1

Given :-

• A car travelling at 36 km/hr speeds upto 54 km/hr in 5 seconds. If the same car stops in 20 s.

To find :-

• Acceleration and retardation of car

Solution :-

A car travelling at 36 km/hr speeds upto 54 km/hr in 5 seconds.

• Initial velocity (u) = 36km/h
• Final velocity (v) = 54km/h
• Time (t) = 5 s

→ Initial velocity = 36km/h

→ u = 36 × 5/18

→ u = 2 × 5

→ u = 10m/s

→ Final velocity = 54 km/h

→ v = 54 × 5/18

→ v = 3 × 5

→ v = 15m/s

According to first equation of motion

→ v = u + at

→ 15 = 10 + a × 5

→ 15 - 10 = 5a

→ 5a = 5

→ a = 5/5 = 1m/s²

Hence,

• Acceleration of car is 1m/s²

If the same car stops in 20 s.

• Retardation = ?
• Final velocity = 0
• Time = 20s

→ v = u + at

→ 0 = 10 + a × 20

→ - 10 = 20a

→ a = - 10/20

→ a = - 0.5m/s²

• Minus shows retardation

Therefore,

• Retardation of car is - 0.5m/s²

Answer 2

GIVEN :-

• ᴀ ᴄᴀʀ ᴛʀᴀᴠᴇʟʟɪɴɢ ᴀᴛ 36 ᴋᴍ/ʜr sᴘᴇᴇᴅs ᴜᴘᴛᴏ 54 ᴋᴍ/ʜr ɪɴ 5 sᴇᴄᴏɴᴅ .

TO FIND :-

1. ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴄᴀʀ .
2. ɪғ ᴛʜᴇ sᴀᴍᴇ ᴄᴀʀ sᴛᴏᴘs ɪɴ 20s, ᴛʜᴇɴ ᴡʜᴀᴛ ɪs ᴛʜᴇ ʀᴇᴛᴀʀᴅᴀᴛɪᴏɴ ?

SOLUTION :-

We have know that,

$\huge\orange\star\:\bf{\gray{\underline{\pink{\boxed{\purple{v\:=\:u\:+\:at\:}}}}}}$

Where,

• v = ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ

• ᴜ = ɪɴɪᴛɪᴀʟ ᴠᴇʟᴏᴄɪᴛʏ

• a = ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ

• t = ᴛɪᴍᴇ

According to the question,

• v = 54 km/h = 54 × 5/18 = 15 m/s

• u = 36 km/h = 36 × 5/18 = 10 m/s

• t = 5 s

=> 15 = 10 + a × 5

=> a × 5 = 15 - 10

=> a = 5/5

=> a = 1 m/s²

$\rm\pink{\therefore}$ 1) ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴄᴀʀ ɪs 1 ᴍ/s² .

$\rule{200}2$

Now, it is given that

• ᴛʜᴇ sᴀᴍᴇ sᴛᴏᴘs ɪɴ 20s .

• Tʜᴇɴ ᴛʜᴇ ғɪɴᴀʟ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ᴄᴀʀ ɪs " 0 ᴍ/s " .

Here,

• v = 0 m/s

• u = 10 m/s

• t = 20 s

=> 0 = 10 + a × 20

=> a × 20 = - 10

=> a = -10/20

=> a = -0.5 m/s²

[Note :- Here, retardation is occured . So acceleration results in -ve .]

$\rm\pink{\therefore}$ 2) Tʜᴇ ʀᴇᴛᴀʀᴅᴀᴛɪᴏɴ ᴏғ ᴛʜᴇ ᴄᴀʀ ɪs " -0.5 ᴍ/s² " .