Question

a car is moving at a velocity of 54 km/h . after 10 seconds the velocity becomes 30km/h . assuming that the change in velocity took place at uniform rate, find the acceleration​

Answer 1

Answer:

The acceleration of the car is –0.67 m/s².

Step-by-Step explanation:

Initial Velocity of Car = 54 kmph

Final Velocity of Car = 30 kmph

Time = 10 seconds

★ Convert the Velocity in m/s -

$\sf{\longrightarrow} \: \dfrac{54}{3.6} = 15 \: m{s}^{ - 1}$

$\sf{\longrightarrow} \: \dfrac{30}{3.6} = 8.3 \: {ms}^{ - 1}$

__________________

$\bigstar \: \sf{Acceleration = \dfrac{v - u}{t}}$

• v = 8.3 m/s
• u = 15 m/s
• t = 10 seconds

$\sf{\longrightarrow} \: \dfrac{8.3 - 15}{10}$

$\sf{\longrightarrow} \: \dfrac{ - 6.7}{10}$

$\sf{\longrightarrow} \: - 0.67 \: {ms}^{ - 2}$

The car is retarding.

Therefore, the acceleration of the car is –0.67 m/s².

Answer 2

QuesTion

• A car is moving at a velocity of 54 km/h. After 10 seconds the velocity becomes 30 km/h. Assuming that the change in velocity took place at uniform rate, find the acceleration of car.

AnsweR

• Acceleration of car is -0.67 m/s².

Step By Step Explanation

Given that

• Initial velocity of car (u) = 54 km/h
• Final velocity of car (v) = 30 km/h
• Time taken by car (t) = 10 seconds

To Find

• Acceleration of car (a)?

Solution

• Here, we have initial velocity of car (u) = 54 km/h = (54 × 5/18) m/s = 15 m/s, Final velocity of car (v) = 30 km/h = (30 × 5/18) m/s = 8.33 m/s and time taken by car (t) = 10 s, we have to find acceleration of car (a). So, here we will use first equation of motion to find it's acceleration.

We know that,

$\pmb{\LARGE{\boxed{\bf{v = u + at}}}}$

★ Putting all values :

⇒ $\sf 8.33 = 15 + a(10)$

⇒ $\sf 8.33 - 15 = 10a$

⇒ $\sf -6.67 = 10a$

⇒ $\sf a = \dfrac{-6.67}{10}$

⇒ a = -0.66

➠ $\pmb{\underline{\boxed{\bf{a = -0.67\:m/s^2}}}}$

∴ Hence, acceleration of a car (a) is -0.67 m/s². (Acceleration came in negative because the car retards).

Know More

$\clubsuit$ Three equations of motion :

1. v = u + at ㅤㅤㅤㅤㅤ[Used above]
2. s = ut + ½ at²
3. v² = u² + 2as

$\clubsuit$ Some important definitions :

• Acceleration

Acceleration is the process where velocity changes. Since, velocity is the speed and it has some direction. So, change in velocity is considered as acceleration.

• Initial velocity

Initial velocity is the velocity of the object before the effect of acceleration.

• Final velocity

After the effect of acceleration, velocity of the object changes. The new velocity gained by the object is known as final velocity.

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