Question

A truck traveling at 54 km/h slows down to 36 km/h in 10 sec. Find retardation.

Answer 1

Question :-

A truck is traveling at 54 km/hr slows down to 36 km/hr in 10 seconds .

Find the retardation ?

Answer :-

Given :-

A truck is traveling at 54 km/hr slows down to 36 km/hr in 10 seconds .

Required to find :-

• Retardation of the truck

Formula used :-

$\large{\boxed{\tt{Acceleration = \dfrac{ Change \; in \; velocity }{ Change \; in \; time }}}}$

Units Conversion :-

Before coming to the solution part we need to convert some units from one unit to another.

Here,

The required physical quantity whose units needed to be converted is speed .

So, convert speed from km/hr into m/s

The formula is ,

$\boxed{\tt{1\;km/hr\;=\; \dfrac{5}{18}\; m/s}}$

So,

54 km/hr = ? m/s

$\implies{\tt{ 54 \times \dfrac{5}{18}}}$

$\implies{\tt{ 3 times 5 }}$

$\red{\implies{\tt{ 15\; m/s}}}$

Similarly,

36 km/hr = ? m/s

$\implies{\tt{ 36 \times \dfrac{5}{18}}}$

$\implies{\tt{ 2 \times 5 }}$

$\red{\implies{\tt{ 10 \; m/s }}}$

Solution :-

In the question it is given that ,

A truck is traveling at 15 m/s slows down to 10 m/s in 10 seconds .

So, from the above we can conclude that ,

Initial velocity ( u ) = 15 m/s

Final velocity ( v ) = 10 m/s

Time (t) = 10 seconds

He asked us to find the retardation of the truck .

Retardation is known as negative acceleration .

I think you may be wondering about what is meant by acceleration .

So, let me explain you about acceleration .

Acceleration is the change in the velocity per unit time .

It's S.I. units are m/s² .

In simple terms we can say that Acceleration occurs when there is change in velocity .

It is represented as ,

$\tt{ acceleration = \dfrac{ change \: in \: velocity }{ Change \: in \; time }}$

$\implies{\rm{ Acceleration = \dfrac{ \Delta v }{ \Delta t }}}$

Here,

∆ This is called as Delta

And , " ∆ " represents change .

So,

Change in velocity is the difference between the final velocity and initial velocity .

So,

∆v = (v) final velocity - (u) initial velocity

Hence,

$\tt{ Acceleration = \dfrac{ 10 \; m/s - 15 \; m/s }{ 10 \; s}}$

$\tt{ Acceleration = \dfrac{ - 5 \; m/s }{10 \: s }}$

$\implies{\red{\underline{ Acceleration = - 0.5 m/s^2 }}}$

Since negative acceleration is known as retardation

Hence,

Retardation = - 0.5 m/s²

Answer 2

Given ,

• Final velocity (u) = 36 km/h or 10 m/s
• Initial velocity (v) = 54 km/h or 15 m/s
• Time (t) = 10 sec

As we know that ,

➡The negative acceleration is called redaration or deacceleration

➡Redaration = (v - u)/t

➡The SI unit redaration is same as the acceleration i.e m/s²

Thus ,

$\sf \Rightarrow a = \frac{10 - 15}{10} \\ \\\sf \Rightarrow a = - \frac{ 5}{10} \\ \\ \sf \Rightarrow a = - 0.5 \: \: m/ {s}^{2}$

$\therefore \bold{ \sf{ \underline{The \: redaration \: is \: -0.5 m/ {s}^{2} }}}$