Question

A car travelling at 67 km/h slows down to 33 km/h in 15 seconds find the retardation

Answer 1

$\large \dag$ Question :-

A car travelling at 67 km/h slows down to 33 km/h in 15 seconds find the retardation.

$\large \dag$ Answer :-

$\red\dashrightarrow\underline{\underline{\sf  \green{Retardation   \: is \:  0.63\: m/s^2 }} }$

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

❒ Converting Velocities in m/s :-

We Have,

$\text{Initial Velocity = 67 \: km/h}$

$\rm = \bigg( 67 \times \frac{5}{18} \bigg) \: m/s$

$\rm = \bigg( \frac{335}{18} \bigg) \: m/s$

$\red{:\longmapsto \rm Initial \: Velocity = 18.62 \: m/s }$

And,

$\text{Final Velocity = 33 \: km/h}$

$\rm = \bigg( 33 \times \frac{5}{18} \bigg) \: m/s$

$\rm = \bigg( \frac{165}{18} \bigg) \: m/s$

$\red{:\longmapsto \rm Final \: Velocity = 9.17 \: m/s }$

Now Here we have :

• Initial Velocity = u = 18.62 m/s

• Final Velocity = v = 9.17 m/s

• Time = t = 15 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 ;

$:\longmapsto \rm 9.17 = 18.62 + a \times 15$

$:\longmapsto \rm 15a = 9.17 - 18.62$

$:\longmapsto \rm 15a = - 9.45$

$:\longmapsto \rm a = \frac{ - 9.45}{ \: 15}$

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf a = - 0.63} }}}$

Hence,

$\large\underline{\pink{\underline{\frak{\pmb{\text Acceleration=-0. 63\: m/s^2 }}}}}$

Here negative sign denotes Retardation

Therefore,

$\large\underline{\pink{\underline{\frak{\pmb{Retardation = 0.63 \: m/s^2 }}}}}$

Answer 2

Answer:

$\sf\tt\large{\green {\underline {\underline{⚘\;Question:}}}}$

1)A car travelling at 67 km/h slows down to 33 km/h in 15 seconds. Find the retardation.

$\sf\tt\large{\purple {\underline {\underline{⚘\;Answer:}}}}$

$\sf\tt\large{\blue {\underline {\underline{\;The \;retardation \;is \;0.63 \;m/s^2:}}}}$

$\sf\tt\large{\red {\underline {\underline{⚘\;Solution:}}}}$

Hey mate,

First let verify your answer.

Next we can start our calculations .

In the question given that A car is travelling at 67km/h slows down to 33 km/h in 15seconds .We should find the retardation.

If we want to find retardation first we should convert velocities in m/s.

Initial velocity =67km/h

Initial velocity =(67×5/18)m/s

Initial velocity =18.62 m/s.

And,

Final velocity =33km/h

Final velocity =(33×5/18 ) m/s

Final velocity =9.17m/s.

Now ,

Here we should come to that to find retardation we should apply the 1st equation of motion formula.

That is,

$\sf\tt\large{\blue {\underline{\underline{⚘\;v \; = \; u + \;at}}}}$

Now ,lets apply all the values we get that,

9.17 =18.62+a×15

15a = 9.17- 18.62

15a =-9.45

a = -9.45/15

a =-0.63

Therefore,

Acceleration =-0.63 m/s.

Here we should come to know that negative values always denotes retardation.

so,

$\sf\tt\large{\purple {\underline {\underline{\;Retardation \;is \;0.63 \;m/s^2:}}}}$