Question

Beginning from rest, Batman accelerates his Bat to reach a velocity of 60 meters per second in 10 seconds. Then he applies the brakes and the velocity of the Batmobile decreases to 10 meters per second in the next 1 second. Calculate the acceleration of the Batmobile in both cases.
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Answer 1

Answer :-

→ Acceleration in 1st case = 6 m/s²

→ Acceleration in 2nd case = -50 m/s²

Explanation :-

For the 1st case :-

We have :-

• Initial velocity (u) = 0 m/s

• Final velocity (v) = 60 m/s

• Time taken (t) = 10 sec

Let's calculate the acceleration of the batmobile by using 1st equation of motion .

⇒ v = u + at

⇒ 60 = 0 + a(10)

⇒ 60 = 10a

⇒ a = 60/10

⇒ a = 6 m/s²

For the 2nd case :-

We have :-

• Initial velocity (u) = 60 m/s

• Final velocity (v) = 10 m/s

• Time taken (t) = 1 sec

Again let's calculate the acceleration in this case by using the 1st equation of motion .

⇒ v = u + at

⇒ 10 = 60 + a(1)

⇒ 10 - 60 = a

⇒ a = -50 m/s²

[Here, -ve sign shows retardation .]

Answer 2

❒ Case - 1 :-

⇝ Given :-

• Batman is initially at rest.

• Batman accelerates his Batmobile to reach a velocity of 60 m/s in 10 seconds.

⇝ To Find :-

• Acceleration of Batmobile

⇝ Solution :-

Here,

• Initial velocity = u = 0 m/s

• Final velocity = v = 60 m/s

• Time taken = t = 10 sec

Let Acceleration be = a m/s²

★ We Have 1st Equation of Motion :

$\large \orange{ \bf v = u + at}$

$:\longmapsto60 = 0 + \text a(10)$

$:\longmapsto60 = 10 \times \text a$

$:\longmapsto\text a = \cancel\frac{60}{10}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf a = 6\:m/s {}^{2} } }}}$

Hence,

$\Large\underline{\pink{\underline{\frak{\pmb{\text Acceleration = 6\:m/s^2 }}}}}$

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❒ Case - 2 :-

⇝ Given :-

• Batman is is moving with velocity 60 m/s.

• He applies the brakes and the velocity of the Batmobile decreases to 10 meters per second in the next 1 second.

⇝ To Find :-

• Acceleration of Batmobile

⇝ Solution :-

Here,

• Initial velocity = u = 60 m/s

• Final velocity = v = 10 m/s

• Time taken = t = 1 sec

Let Acceleration be = a m/s²

★ We Have 1st Equation of Motion :

$\large \orange{ \bf v = u + at}$

$:\longmapsto10 = 60 + \text a(1)$

$:\longmapsto10 = 60 + \text a$

$:\longmapsto\text a = 10 - 60$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf a = -50\:m/s {}^{2} } }}}$

Hence,

$\Large\underline{\pink{\underline{\frak{\pmb{\text Acceleration = -50\:m/s^2 }}}}}$

Note : Negative Sign Denotes Retardation