Question

calculate the acceleration of a bus traveling with a velocity of 15m-¹ which then slows down to attain a velocity of 7m-¹ in 2 s.​

Answer 1

⇝ Given :-

• A bus is traveling with an initial velocity of 15 m/s

• Then it slows down to attain a velocity of 7 m/s in 2 s.

⇝ To Find :-

• Acceleration of the Bus.

⇝ Solution :-

Here,

• Initial Velocity = u = 15 m/s

• Final Velocity = v = 7 m/s

• Time Taken = t = 2 s

Let Acceleration of Bus be = a m/s².

❒ We Have 1st Equation of Motion as :

$\large \bf \red \bigstar \: \: \orange{ \underbrace{ \underline{v = u + at}}}$

⏩ Applying 1st Equation of Motion ;

$:\longmapsto7 = 15 + \text a \times 2$

$:\longmapsto2\text a = 7 - 15$

$:\longmapsto2\text a = - 8$

$:\longmapsto\text a = \cancel\frac{ - 8}{ \: \: \: 2}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf a = - 4 \: m/s^2} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Acceleration = - 4 \: m/s^2}}}}}$

Note : -ve sign represents the Retardation.

Additional Information :-

Three Equations of Motion :

$\large \green{\qquad \boxed{\boxed{\begin{array}{cc} \maltese \: \: \bf v = u + at \\ \\ \maltese \: \: \bf s = ut + \dfrac{1}{2}a {t}^{2} \\ \\ \maltese \: \: \bf{v}^{2} - {u}^{2} = 2as\end{array}}}}$

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Answer 2

Question:

• Calculate the acceleration of a bus traveling with a velocity of 15 m/s which then slows down to attain a velocity of 7 m/s in 2 s.

Answer:

• Acceleration of a bus is -4 m/s².

Explanation:

Given that:

• Initial velocity (u) = 15 m/s
• Final velocity (v) = 7 m/s
• Time taken (t) = 2 s

To Find:

• Acceleration (a)?

Solution:

• Using first equation of motion ::

We know that,

⧪ $\boxed{\bf{\purple{v = u + at}}}$ ⧪

Where,

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

According to the question by using the formula we get,

➼ $\sf 7 = 15 + (a\:\times\:2)$

➼ $\sf 7 - 15 = 2a$

➼ $\sf 2a = -8$

➼ $\sf a = {\cancel{\dfrac{-8}{2}}}$

➼ $\bf\pink{a = -4\:m/s^2}$

∴ Acceleration of a bus is -4 m/s².

Learn More:

$\clubsuit$ Three equations of motion :

1. v = u + at ㅤㅤㅤㅤㅤ[Used above]
2. s = ut + ½ at²
3. v² = u² + 2as

$\clubsuit$ Some important definitions :

• Acceleration

Acceleration is the process where velocity changes. Since, velocity is the speed and it has some direction. So, change in velocity is considered as acceleration.

• Initial velocity

Initial velocity is the velocity of the object before the effect of acceleration.

• Final velocity

After the effect of acceleration, velocity of the object changes. The new velocity gained by the object is known as final velocity.

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