Question

a car traveling at 180km/hr is uniformly retarded and brought to rest 7.5 sec. find its acceleration and distance coming to rest​

Answer 1

Given :

▪ Initial velocity of car = 180kmph

▪ Time interval = 7.5s

To Find :

▪ Acceleration of car.

▪ Distance travelled by car.

Concept :

☞ Acceleration is defined as the rate of change in velocity.

☞ It is a vector quantity.

☞ It can be positive/negative or zero.

☞ It has both magnitude as well as direction.

☞ Since, acceleration has said to be constant, we can easily apply ewuation of kinematics to solve this type of questions.

Third equation of kinematics :

$\bigstar\:\underline{\boxed{\bf{\red{v^2-u^2=2as}}}}$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• s denotes distance

Conversion :

↗ 1kmph = 5/18mps

↗ 180kmph = 180×5/18 = 50mps

Calculation :

☢ Acceleration of car :

$\dashrightarrow\sf\:a=\dfrac{v-u}{t}\\ \\ \dashrightarrow\sf\:a=\dfrac{0-50}{7.5}\\ \\ \dashrightarrow\underline{\boxed{\bf{a=-6.67\:ms^{-2}}}}\:\orange{\bigstar}$

[Note : -ve sign shows retardation.]

☢ Distance travelled by car :

$\longrightarrow\sf\:v^2-u^2=2(-a)s\\ \\ \longrightarrow\sf\:(0)^2-(50)^2=-2(6.67)(s)\\ \\ \longrightarrow\sf\:s=\dfrac{(50)^2}{2\times 6.67}\\ \\ \longrightarrow\underline{\boxed{\bf{s=187.4\:m}}}\:\orange{\bigstar}$

Answer 2

GIVEN:

• Initial velocity = 180km/h = 50m/s
• Time = 7.5 s
• Final velocity = 0 m/s

TO FIND:

• Acceleration of the car
• Distance travelled by car

SOLUTION:

Here , given acceleration in negative that means the car has retardation.

Using the third kinematic equation

v² - u² = 2as

Where

• v ➪ Final velocity
• u ➪ initial velocity
• a ➪ Retardation ( °.° Given acceleration in negative )
• s ➪ distance travelled

Finding acceleration

a = v - u/t

⟶ a = 0 - 50/7.5

⟶ a = -6.67 m/s²

➦ Finding Distance travelled by car

➜ v² - u² = 2(-a)(s)

Note : Where -a indicates retardation

➜ 0² - 50² = 2(6.67)(s)

➜ - 2500/-13.34 = s

➻ s = 187.4 m

Hence, acceleration = -6.67 m/s² & distance travelled by car = 187.40 m