Question

A car travelling at 110 km/h decelerates for 4.5 seconds to a final velocity of 45 km/h. Calculate the deceleration of the car

Answer 1

$\large \dag$ Question :-

A car travelling at 110 km/h decelerates for 4.5 seconds to a final velocity of 45 km/h. Calculate the deceleration of the car.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Deacceleration   \:  is \:  4 \: m/s^2}} }$

$\large \dag$ Step by step Explanation :-

❒ Converting Velocities in m/s :-

We Have,

$\text{Initial Velocity= 110 km/h}$

$= \rm\bigg( 110\times \frac{5}{18}\bigg)second$

$\red{:\longmapsto \text{Time = 30.5 \:m/s}}$

Also,

$\text{Final Velocity= 45 km/h}$

$= \rm\bigg( 45\times \frac{5}{18}\bigg)second$

$\red{:\longmapsto \text{Time = 12.5 \:m/s}}$

Now Here we have :

• Initial Velocity = u = 30.5 m/s

• Final Velocity = v = 12.5 m/s

• Time = t = 4.5 s

• Let acceleration be = a m/s²

❒ We Have 1st Equation of Motion as :

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

⏩ Applying 1st Equation of Motion ;

$\\ :\longmapsto \rm 12.5 = 30.5 + a \times 4.5$

$:\longmapsto \rm 12.5 - 30.5 = 4.5a$

$:\longmapsto \rm 4.5a = - 18$

$:\longmapsto \rm a = \frac{ - 18}{ \: \: 4.5}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf a = -4} }}}$

⇝ Acclerration is - 4 m/s²

Therefore,

$\large\red\maltese\:\:\underline{\pink{\underline{\frak{\pmb{Deacceleration =4\: m/s^2 }}}}}$

Answer 2

Given : A car travelling at 110 km/h decelerates for 4.5 seconds to a final velocity of 45 km/h. Calculate the deceleration of the car

Need to Find : The deceleration of the car

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★ Cᴏɴᴄᴇᴘᴛ :

According to the question, here we are given that the initial velocity of the car is 110 km/h and it decelerates for 4.5 sec to reach the final velocity which is 45 km/h.

Now, we need to use the first equation of motion to get the deceleration. Putting all the required values we can find the acceleration and from there we need to change into deceleration by putting the -ve sign in front of the value.

★ Sᴏʟᴜᴛɪᴏɴ :

Given Data

• Initial Velocity (u) = 110 km/h

As we can see that the initial vel is in km/h instead of m/sec. So, let's convert km/h into m/sec

Conversion : 1 km/h = 5/18 m/sec

Hence, 110 km/h = 110 × 5/18 m/sec = 55 × 5/9 = 30.5 m/sec

• Final Velocity (v) = 45 km/h

Again, the final vel is in km/h instead of m/sec. So, let's convert km/h into m/sec

Conversion : 1 km/h = 5/18 m/sec

Hence, 45 km/h = 45 × 5/18 m/sec = 25/2 = 12.5 m/sec

• Time (t) = 4.5 sec

Calculation Begins

According to the first equation of motion we get to know that the ingredients are initial velocity, final velocity, time and acceleration. All the three components are given leaving the acceleration.

So, the equation is ⤵

★ v = u + at ★

Here, a refers acceleration

• 12.5 = 30.5 + a(4.5)

• 30.5 - 12.5 = -4.5a

• -4.5a = 18

• a = -18/4.5

• a = -4

As the acceleration is -4.5

So, adding -ve sign in front of the value we get deceleration

• Deceleration = -(-4) = 4

❒ Hence, the deceleration of the car is 4 m/sec