Question

A CAR ARCHIVES AT A SPEED OF 40M/S BY undergoing acceleration of 5 m//s in 3 s. find the initial speed of the car

Answer 1

Correct Question:

A car achieves at a speed of 40 m/s by undergoing acceleration of 5 m/s² in 3 s. Find the initial speed of the car?

Answer:

• The initial speed (u) of the car is 25 m/s

Given:

• Final velocity (v) = 40 m/s.
• Time taken (t) = 3 seconds.
• Acceleration produced (a) = 5 m/s²

Explanation:

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From the First Kinematic Equation, we know

⇒ v = u + a t

Where,

• v Denotes Final velocity.
• u Denotes Initial velocity.
• a Denotes Acceleration.
• t Denotes Time taken.

Substituting the values,

⇒ 40 = u + ( 5 × 3 )

⇒ 40 = u + 15

⇒ 40 - 15 = u

⇒ u = 40 - 15

⇒ u = 25

⇒ u = 25 m/s

∴ The initial speed (u) of the car is 25 m/s.

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Extra:

Question: Let's find the Distance which car has to travel to achieve Final velocity?

Answer:

From the Second Kinematic Equation, we know

⇒ v² = u² + 2 a s

Where,

• v Denotes Final velocity.
• u Denotes Initial velocity.
• a Denotes Acceleration.
• s Denotes Distance travelled.

Substituting the values,

⇒ (40)² = (25)² + 2 × 5 × s

⇒ 1600 = 625 + 10 s

⇒ 10 s = 1600 - 625

⇒ 10 s = 975

⇒ s = 975 / 10

⇒ s = 97.5

⇒ s = 97.5 m

∴ The Distance travelled by the car is 97.5 m.

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Answer 2

Gɪᴠᴇɴ

Final velocity = 40 m/s

Acceleration = 5 m/s²

Time = 3 seonds.

Tᴏ ꜰɪɴᴅ

Initial velocity of the car

Sᴏʟᴜᴛɪᴏɴ

According to Equation of Motion :

Final velocity is equal to sum of initial velocity & product of acceleration & time.

⇒ v = u + at

Here, v denotes final velocity, u denotes initial velocity, a denotes acceleration & t denotes time.

Pᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇꜱ ᴡᴇ ɢᴇᴛ :

⇒ 40 = u + (5 × 3)

⇒ 40 = u + 15

⇒ u = 40 - 15

⇒ u = 25 m/s

Tʜᴇʀᴇꜰᴏʀᴇ,

Initial velocity of car = 25 m/s

Sᴏᴍᴇ ᴍᴏʀᴇ ꜰᴏʀᴍᴜʟᴀꜱ :

⇾ a = (v - u)/t

⇾ s = ut + ½at²

⇾ v² - u² = 2as

Some more informations :

Dimensional formula of velocity : m/s

Dimensional formula of acceleration : m/s²

Velocity = Distance/time

= m/s or, km/h

Acceleration = (∆Velocity/time)

= (m/s)/s

= m/s² or, km/h²