Question

Question

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

Proper Explanation Required
Answer is 0.63 m/s²

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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,

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

Answer 2

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

Need to Find : The retardation or negative acceleration of the car

Question states that the car is traveling at an initial velocity (u) of 67 km/h and later it slows down to 33 km/h which is the final velocity (v), time taken is 15 sec.

_______________________________

Given Data :

Initial Velocity (u) = 67 km/h ⟹ 67 × 5/18 ⟹ 18.62 m/sec

Final Velocity (v) = 33 km/h ⟹ 33 × 5/18 ⟹ 9.17 m/sec

Time taken (t) = 15 sec

As the time is in seconds we need to convert the velocities into m/sec. We can convert time in hr but converting velocities is more preferable.

Cᴏɴᴠᴇʀsɪᴏɴ :

1 km/h = 5/18 m/sec

Calculation Begins :

Using the first equation of motion. Here only first equation is applicable because distance is not provided.

☯ First Equation : v = u + at

a is the acceleration

Putting the values we get

• 9.17 = 18.62 + a(15)

• 15a = 18.62 - 9.17

• 15a = - 9.45

• a = - 0.63

As the acceleration is -0.63 m/sec so, the negative acceleration or retardation should be the opposite of it

Henceforth, retardation is 0.63 m/sec