Question

Abody move with a steady increase of velocity from 28.8km/h to 72km/h in 6 seconds. what is its acceleration?

Answer 1

Answer:

• 2m/s² is the required acceleration.

Explanation:

Given :

• Initial velocity ,u = 28.8km/h
• Final velocity ,v = 72km/h
• Time taken ,t = 6

To Find :

• Acceleration ,a

Solution :

According to the Question

It is given that body move with a steady increase of velocity from 28.8km/h to 72km/h in 6 seconds.

We have to calculate the acceleration of the body.

Firstly we change the unit here.

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Initial velocity ,u = 28.8×5/18 = 8m/s

Final velocity ,v = 72×5/18 = 20m/s

Now, calculating the acceleration

As we know that acceleration is defined as the rate of change in velocity.

• a = v-u/t

where,

• v is the final velocity
• a is the acceleration
• u is the initial velocity
• t is the time taken

Substitute the value we get

→ a = 20-8/6

→ a = 12/6

→ a = 2m/s².

• Hence, the acceleration of the body is 2m/s².

Answer 2

Answer:

Given :-

• A body move with a steady increase of velocity from 28.8 km/h to 72 km/h in 6 seconds.

To Find :-

• What is the acceleration.

Formula Used :-

$\clubsuit$ First Equation Of Motion Formula :

$\mapsto \sf\boxed{\bold{\pink{v =\: u + at}}}$

where,

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = Time

Solution :-

First, we have to convert initial velocity and final velocity km/h into m/s :

${\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: initial \: velocity\: :-}}}}}$

$\implies \sf Initial\: Velocity =\: 28.8\: km/h$

$\implies \sf Initial\: Velocity =\: 28.8 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Initial\: Velocity =\: \dfrac{288}{10} \times \dfrac{5}{18}\: m/s$

$\implies \sf Initial\: Velocity =\: \dfrac{\cancel{1440}}{\cancel{180}}\: m/s$

$\implies \sf\bold{\green{Initial\: Velocity =\: 8\: m/s}}$

${\small{\bold{\purple{\underline{\bigstar\: In\: case\: of\: final\: velocity\: :-}}}}}$

$\implies \sf Final\: Velocity =\: 72\: km/h$

$\implies \sf Final\: Velocity =\: 72 \times \dfrac{5}{18}\: m/s\: \: \bigg\lgroup \sf\bold{\pink{1\: km/h =\: \dfrac{5}{18}\: m/s}}\bigg\rgroup$

$\implies \sf Final\: Velocity =\: \dfrac{\cancel{360}}{\cancel{18}}\: m/s$

$\implies \sf\bold{\green{Final\: Velocity =\: 20\: m/s}}$

Now, we have to find the acceleration of body :-

Given :

• Final Velocity (v) = 20 m/s
• Initial Velocity (u) = 8 m/s
• Time = 6 seconds

According to the question by using the formula we get,

$\longrightarrow \sf 20 =\: 8 + a(6)$

$\longrightarrow \sf 20 =\: 8 + 6a$

$\longrightarrow \sf 20 - 8 =\: 6a$

$\longrightarrow \sf 12 =\: 6a$

$\longrightarrow \sf \dfrac{\cancel{12}}{\cancel{6}} =\: a$

$\longrightarrow \sf 2 =\: a$

$\longrightarrow \sf\bold{\red{a =\: 2\: m/s^2}}$

$\therefore$ The acceleration of body is 2 m/s².