Question

An object is initially moving at an unknown velocity. It accelerates at a rate of 2.0 m/s² to a new velocity of 45 m/s in 10 s. What was the initial velocity?

Answer 1

Answer:-

$\red{\bigstar}$ Initial velocity $\large\leadsto\boxed{\rm\green{25 \: m/s}}$

• Given:-

• Acceleration = 2 m/s²
• Final velocity = 45 m/s
• Time = 10 sec.

• To Find:-

• Initial velocity = ?

• Solution:-

✴ Initial velocity:-

We know,

• First Equation of motion:-

$\blue{\bigstar}$ $\large\underline{\boxed{\bf\pink{v = u + at}}}$

where,

• v = final velocity
• u = initial velocity
• a = acceleration
• t = time taken

• Substituting in the values:-

➙ $\sf 45 = u + 2 \times 10$

➙ $\sf 45 = u + 20$

➙ $\sf u = 45 - 20$

★ $\bf\red{u = 25 \: m/s}$

Therefore, the initial velocity is 25 m/s.

Answer 2

Answer:

✯ Given :-

• An object is initially moving at an unknown velocity. It's accelerates at a rate of 2.0 m/s² to a new velocity of 45 m/s in 10 secs.

✯ To Find :-

• What is the initial velocity.

✯ Formula Used :-

$\boxed{\bold{\large{✮\: v\: =\: u\: +\: at\: ✮}}}$

✯ Solution :-

⋆ Given :

• Final velocity (v) = 45 m/s
• Acceleration (a) = 2 m/s²
• Time (t) = 10 secs

➣ According to the question by using the formula we get,

⇒ 45 = u + 2 × 10

⇒ 45 = u + 20

⇒ u = 45 - 20

➠ u = 25 m/s

$\therefore$ The initial velocity is 25 m/s .

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✪ Extra Information ✪

✧ 1st equation of motion :-

$\large\purple{\underline{{\boxed{\textbf{v\: =\: u\: +\: at}}}}}$

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time taken

✧ 2nd equation of motion :-

$\large\green{\underline{{\boxed{\textbf{s\: =\: ut\: +\: ½\: at²}}}}}$

where,

• s = Distance covered
• u = Initial velocity
• t = Time taken

✧ 3rd equation of motion :-

$\large\red{\underline{{\boxed{\textbf{v²\: -\: u²\: =\: 2as}}}}}$

where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• s = Distance covered

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