Question

8. A car is traveling with a speed of 36km/h. the driver applies the brakes and retards the car uniformly. The car is stopped in 5s. Find (i) the retardation of the car Distance traveled before it is stopped after applying the brakes. 9. A train is traveling at a speed of 72km/h. The driver applies brakes so that a Uniform acceleration of - 0.2ms-2 is produced. Find the distance traveled by the train before it comes to rest.​

Answer 1

$\\ \huge{ \underline{ \underline{ \sf{ \pmb{Question \: (1)}}}}}$

8. A car is traveling with a speed of 36km/h. The driver applies the brakes and retards the car uniformly. The car is stopped in 5s. Find :-

(i) The retardation of the car .

(ii) Distance traveled before it is stopped after applying the brakes.

$\\ \huge{ \underline{ \underline{ \sf{ \pmb{Required \: Answer}}}}}$

$\\ \large{\underline{ \underline{ \tt{Given}}}}$

• Initial velocity of the car u = 36km/h
• Final Velocity of the car v = 0 m/s
• Time t = 5s

$\\ \large{ \underline{ \underline{ \tt{To \: Find}}}}$

• The retardation of the car .
• Distance traveled before it is stopped after applying the brakes.

$\\ \large{ \underline{ \underline{ \tt{Formula \: Used}}}}$

• $\sf{ \pmb{v = u + at}}$
• $\sf{ \pmb{s = ut + \dfrac{1}{2} a {t}^{2}}}$

Where,

• v = Final velocity
• u = initial velocity
• a = acceleration
• t = time
• s = distance

$\\ \large{ \underline{ \underline{ \tt{Solution}}}}$

We were given that:-

• The car is traveling with a speed of 36km/h

First, converting the units in SI :-

$\sf{initial \: velocity \: \bold{u} = \dfrac{36km}{h} = \dfrac{(36 \times 1000)m}{3600s} = \dfrac{10m}{s} = \bold{10ms {}^{ - 1}}}$

Now, when the driver applies the brakes and retards the car uniformly, the final velocity becomes = 0m/s

From the definition of acceleration:-

$\\ \sf{ \bold{v = u + at}}$

Substituting the values:-

$\\ \tt{\implies{0 = 10 + a \times 5}}$

$\\ \tt{\implies{a = \dfrac{ - 10}{5} \: m {s}^{ - 2}}}$

$\\ \tt{\therefore{\bold{\red{a = - 2 \:m {s}^{ - 2}}}}}$

Negative acceleration indicates retardation.

$\\ \underline{\boxed{\rm{Hence, \: retardation\: of \: the \: car\: is \:\green {2 {ms}^{ - 2}} }}}$

Again,

Distance travelled by the car:-

$\\ \sf{\bold{s = ut + \dfrac{1}{2} a {t}^{2}}}$

Here,

• Initial velocity = 10m/s
• Acceleration a = -2 ms^(-2)
• Time t = 5s

Substituting the values:-

$\\ \tt{\implies{s = 10 \times 5 + ( - 2) \times {5}^{2}}}$

$\\\tt{\implies{s = 5 - 25}}$

$\\ \tt{\therefore{\red{\bold{s = 25m}}}}$

$\\ \underline{\boxed{\rm{Hence, distance \: travelled \: by \: the \: car \: is \: \green{25m}}}}$

$\\ \huge{ \underline{ \underline{ \sf{ \pmb{Question \: (2)}}}}}$

9. A train is traveling at a speed of 72km/h. The driver applies brakes so that a uniform acceleration of - 0.2ms(-2) is produced. Find the distance traveled by the train before it comes to rest.

$\\ \huge{ \underline{ \underline{ \sf{ \pmb{Required \: Answer}}}}}$

$\\ \large{\underline{ \underline{ \tt{Given}}}}$

• Initial velocity u = 72km/h
• Final velocity v = 0 m/s
• Acceleration a = -0.2ms^(-2)

$\\ \large{ \underline{ \underline{ \tt{To \: Find}}}}$

• Distance traveled by the train.

$\\ \large{ \underline{ \underline{ \tt{Formula \: Used}}}}$

• $\sf{\pmb{ {v}^{2} = {u}^{2} + 2as}}$

$\\ \large{ \underline{ \underline{ \tt{Solution}}}}$

We were given that:-

• The car is traveling with a speed of 72km/h

First, converting the units in SI :-

$\sf{Initial \: velocity \: \bold{u} = \dfrac{72km}{h} = \dfrac{(72 \times 1000)m}{3600s} = \dfrac{20m}{s} = \bold{20ms {}^{ - 1}}}$

Now, when the driver applies the brakes and retards the car uniformly, the final velocity becomes = 0m/s

According to the 3rd equation of motion,

$\\ \bold{ {v}^{2} = {u}^{2} + 2as}$

Substituting the values:-

$\\ \tt{\implies{ {0}^{2} = {20}^{2} + 2 \times ( - 0.2) \times s}}$

$\\ \tt{\implies{0 = 400 - 0.4s}}$

$\\ \tt{\implies{s = \frac{400}{ 0.4}}}$

$\\\tt{\therefore{\bold{\red{s = 1000m }\: or \: \red{1km}}}}$

$\\ \underline{\boxed{\rm{Hence, distance \: travelled \: by \: the \: train \: is \: \green{1km}}}}$