Question

Velocity time graph of a body is shown in the figure. Find its acceleration in m/s2.
I mislabeled it 2 times.. wrong flair... looking forward for answer

Answer 1

Answer :-

Acceleration of the body is 0.0042 m/s² .

Explanation :-

From the graph, we have :-

→ Initial velocity of the body (v₁) = 20 m/s

→ Final velocity of the body (v₂) = 80 m/s

→ Time interval (t) = 4 hrs

= 4(3600)

= 14400 s

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Now, we know that :-

Acceleration = Change in Velocity/Time

⇒ a = ∆v/t

⇒ a = (v₂ - v₁)/t

⇒ a = (80 - 20)/14400

⇒ a = 60/14400

⇒ a = 6/1440

⇒ a = 0.0042 m/s²

Some Extra Information :-

The 3 equations of motion, for a body moving with uniform acceleration are :-

• v = u + at

• s = ut + ½at²

• v² - u² = 2as

Answer 2

Answer:

Given :-

• Initial velocity (u) = 20 m/s
• Final velocity (v) = 80 m/s
• Time (t) = 4 hrs

To Find :-

• What is the acceleration in m/s².

Formula Used :-

$\clubsuit$ Constant Acceleration Formula :

$\longmapsto \sf\boxed{\bold{\pink{a =\: \dfrac{(v - u)}{t}}}}$

where,

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

Solution :-

First, we have to convert the time into seconds :

$\implies \sf Time =\: 4\: hrs$

$\implies \sf Time =\: 4 \times 3600\: seconds\: \bigg\lgroup \bold{\purple{1\: hours =\: 3600\: seconds}}\bigg \rgroup$

$\implies \sf\bold{\red{Time =\: 14400\: seconds}}$

Given :

• Final velocity = 80 m/s
• Initial velocity = 20 m/s
• Time = 14400 seconds

According to the question by using the formula we get,

$\dashrightarrow \sf a =\: \dfrac{(80 - 20)}{14400}$

$\dashrightarrow \sf a =\: \dfrac{6\cancel{0}}{1440\cancel{0}}$

$\dashrightarrow \sf a =\: \dfrac{\cancel{6}}{\cancel{1440}}$

$\dashrightarrow \sf a =\: \dfrac{\cancel{3}}{\cancel{720}}$

$\dashrightarrow \sf\bold{\red{a =\: 0.0042\: m/s^2}}$

$\therefore$ The acceleration is 0.0042 m/s².