Question

an ostrich can aquire a velocity of 144 kmph in 2 sec while leopard can acquire a velocity of 108 kmph in 3sec find ratio of an accelarition

Answer 1

Given :

Final velocity of ostrich = 144km/h

[Time of journey = 2s]

Final velocity of leopard = 108km/h

[Time of journey = 3s]

To Find :

We have to find ratio of their acceleration$.$

SoluTioN :

⟶ Acceleration is defined as the rate of change of speed.

⟶ It is a vector quantity having both magnitude as well as direction.

⟶ SI unit : m/s²

◈ Conversion :

➠ 1 km/h = 5/18 m/s

➠ 144 km/h = 144 × 5/18 = 40 m/s

➠ 108 km/h = 108 × 5/18 = 30 m/s

✭ Acceleration of ostrich :

⇒ a = (v - u) / t

⇒ a = (40 - 0) / 2

⇒ a = 20 m/s²

✭ Acceleration of leopard :

⇒ a' = (v - u) / t

⇒ a' = (30 - 0) / 3

⇒ a' = 10 m/s²

✭ Ratio of their acceleration :

➝ a/a' = 20/10

➝ a : a' = 2 : 1

Answer 2

$\huge\sf\pink{Answer}$

☞ Ratio of their acceleration is equal to 2:1

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$\huge\sf\blue{Given}$

✭ Final Velocity of Ostrich = 144 km/h & it took 2 sec

✭ Final Velocity of Leopard = 108 km/h which took 3 eec

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$\huge\sf\gray{To \:Find}$

◈ Ratio of their acceleration?

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$\huge\sf\purple{Steps}$

So here we shall first convet the speeds to m/s

➝ $\sf 144 \ km/h = 144\times \dfrac{5}{18} = 40 \ m/s$

➝ $\sf 108 \ km/h = 108\times \dfrac{5}{18} = 30 \ m/s$

So now to find the acceleration we shall use the first equation of motion, that is,

$\underline{\boxed{\sf v = u+at}}$

☯ Acceleration of Ostrich

»» $\sf v = u+at$

»» $\sf 40 = 0+a\times 2$

»» $\sf 40 = 2a$

»» $\sf \dfrac{40}{2} = a$

»» $\sf \green{a^1 = 20 \ m/s^2}$

☯ Acceleration of Leopard

➢$\sf v = u+at$

➢ $\sf 30 = 0+a\times 3$

➢ $\sf 30 = 3a$

➢ $\sf \dfrac{30}{3} = a$

➢ $\sf \red{a^2=10 \ m/s^2}$

Their Ratio of Acceleration

➳ $\sf a^1:a^2 = 20:10$

➳ $\sf \orange{Ostrich : Leopard = 2:1}$

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