Question

The velocity of a body changes from 65 m/s - 98 m/s by Time of 12 s . What is distance covered by body if acceleration is 2.75 m/s2.​

Answer 1

Explanation:

According to the Question

It is given that

• Initial velocity ,u = 65m/s
• Final velocity ,v = 98m/s
• Time taken ,t = 12s
• Acceleration ,a = 2.75m/s²

We have to calculate the distance covered by body.

we will use here kinematics equation of motion.

• v² = u² + 2as

Where v is the final velocity

a is the acceleration

u is the initial velocity

v is the final velocity

s is the displacement of the body

Substitute the value we get

=> 98² = 65²+ 2*2.75*s

=> 98² - 65² = 2*2.75*s

=> (98-65)(98+65) = 5.5 *s

=> 33*163 = 5.5 × s

=> 5379 = 5.5 ×s

=> s = 5379/5.5

=> s = 978m

• Hence, the distance covered by the body is 978 metres.

Answer 2

Question:

• The velocity of a body changes from 65 m/s - 98 m/s by time of 12 s. What is distance covered by body if acceleration is 2.75 m/s².

Answer:

• Distance covered by body if acceleration is 2.75 m/s² is 978 m.

Explanation:

Given that:

• Initial velocity (u) = 65 m/s
• Final velocity (v) = 98 m/s
• Time taken (t) = 12 s
• Acceleration (a) = 2.75 m/s²

To Find:

• Distance covered (s)?

Solution:

• Using second equation of motion ::

We know that,

⧪ $\boxed{\bf{\purple{s = ut + \dfrac{1}{2}\:at^2}}}$ ⧪

Where,

• s denotes distance covered
• u denotes initial velocity
• t denotes time taken
• a denotes acceleration

According to the question by using the formula we get,

➼ $\sf s = (65\:\times\:12) + \Bigg\{\dfrac{1}{2}\:\times\:2.75\:\times\:(12)^2\Bigg\}$

➼ $\sf s = 780 + \Bigg\{\dfrac{1}{\cancel{2}}\:\times\:2.75\:\times\:\cancel{144}\Bigg\}$

➼ $\sf s = 780 + (2.75\:\times\:72)$

➼ $\sf s = 780 + 198$

➼ $\bf\pink{ s = 978\:m}$

∴ Hence, distance covered by body if acceleration is 2.75 m/s² is 978 m.

Additional Information:

$\clubsuit$ Three equations of motion ::

1. v = u + at
2. s = ut + ½ at²ㅤㅤ[Used above]
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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