Question

An object is moving with velocity of 10m/s. Its acceleration is 2m/s2. What velocity will be acquired after 5 seconds

Answer 1

Given :

• Initial velocity = 10 m/s
• Acceleration = 2 m/s²
• Time Taken = 5 s

To find :

The Final Velocity of the object .

Solution :

To find the Acceleration :

We know the first Equation of Motion i.e,

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

Where :

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

Using the first Equation of Motion and substituting the values in it, We get :

$:\implies \bf{v = u + at}$

$:\implies \bf{v = 10 + 2 \times 5}$

$:\implies \bf{v = 10 + 10}$

$:\implies \bf{v = 20}$

$\boxed{\therefore \bf{Velocity\:(v) = 20\:m/s}}$

Hence, the final Velocity is 20 m/s.

Alternative method :

First from second Equation of Motion, we will find the distance covered and then by using the third Equation of Motion, we can find the final Velocity of the object.

To find the distance traveled :

We know the second Equation of Motion i.e,

$\boxed{\bf{S = ut + \dfrac{1}{2}at^{2}}}$

Using the Second equation of motion and substituting the values in it, we get :

$:\implies \bf{S = ut + \dfrac{1}{2}at^{2}}$

$:\implies \bf{S = 10 \times 5 + \dfrac{1}{2} \times 2 \times 5^{2}}$

$:\implies \bf{S = 50 + \dfrac{1}{2} \times 2 \times 25}$

$:\implies \bf{S = 50 + \dfrac{1}{\not{2}} \times \not{2} \times 25}$

$:\implies \bf{S = 50 + 25}$

$:\implies \bf{S = 75}$

$\boxed{\therefore \bf{S = 75}}$

Hence the distance traveled is 75 m.

To find the final Velocity :

$\boxed{\bf{v^{2} = u^{2} + 2aS}}$

Where :

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• S = Distance

$:\implies \bf{v^{2} = 10^{2} + 2 \times 2 \times 75}$

$:\implies \bf{v^{2} = 100 + 2 \times 2 \times 75}$

$:\implies \bf{v^{2} = 100 + 300}$

$:\implies \bf{v^{2} = 400}$

$:\implies \bf{v = \sqrt{400}}$

$:\implies \bf{v = 20}$

$\boxed{\therefore \bf{Velocity\:(v) = 20\:m/s}}$

Hence, the final Velocity is 20 m/s.