Question

a particle moves with the velocity of 72 kilometre per hour and acquires a velocity of 108 kilometre per hour in a time interval of 20 minutes determine the acceleration of the particle and the distance travelled by the particle.​

Answer 1

Given :-

Initial velocity = 72 km/h

Final velocity = 108 km/h

Time period to change velocity = 20min

To find :-

• Acceleration
• Distance travelled

Solution :-

Firstly finding acceleration

Using first equation of motion.

v = u + at

Where

• v : final velocity = 108 km/h
• u : initial velocity = 72 km/h
• a : acceleration = ?
• t : time = 20 min = 0.33 hrs

Substituting the values we have

→ 108 = 72 + a(0.33)

→ 108 - 72 = a(0.33)

→ 36 ÷ 0.33 = a

→ acceleration = 109.09 km/h² = 0.008 m/s²

Now , finding distance travelled

Using 3rd equation of motion

S = ut + 1/2 at²

→ S = 72(0.33) + 1/2(109.09)(0.33)²

→ S = 23.7 + 5.93

→ Distance = 29.63 km ≈ 30 km

Hence , distance travelled = 30 km & acceleration = 109.09 km/h².

Answer 2

Answer

Given -

$\bf u = 72 km/hr = 20 m/s$

$\bf v = 108 km/hr = 30 m/s$

$\bf t = 20 mins = 1200 sec$

where

$\longrightarrow$u is initial velocity.

$\longrightarrow$v is final velocity.

$\longrightarrow$t is time taken.

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To find -

1. Acceleration $\longrightarrow$ a

2. Distance travelled $\longrightarrow$ s

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Formula used -

1st equation of motion$\longrightarrow$ $\bf v = u + at$

2nd equation of motion $\longrightarrow$$\bf v^2 = u^2 + 2as$

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Solution -

Substituting the value in the equation -

$\longrightarrow$$\bf u = 20 m/s$

$\longrightarrow$$\bf v = 30 m/s$

$\longrightarrow$$\bf t = 1200 sec$

Substituting the value in the equation -

$\bf v = u + at$

$\implies$$\bf 30 = 20 + 1200a$

$\implies$$\bf 10 = 1200a$

$\implies$$\bf a = 0.0083$

Acceleration of particle is $\bf 0.008 m/s^2$

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$\longrightarrow$$\bf u = 20 m/s$

$\longrightarrow$$\bf v = 30 m/s$

$\longrightarrow$$\bf a = 0.0083 m/s^2$

Substituting the value in equation -

$\bf v^2 = u^2 + 2as$

$\implies$$\bf 30^2 = 20^2 + 2 \times 0.008 s$

$\implies$$\bf 900 = 400 + 2 \times 0.008 s$

$\implies$$\bf 500 = 2 \times 0.008 s$

$\implies$$\bf 250 = 0.008s$

$\implies$$\bf s = \dfrac{250}{0.008}$

$\implies$$\bf s = 30000 m = 30 km.$

Distance travelled by particle is 30 km.

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