Question

a body moving with uniform acceleration of 2m/s² has covered a distance of 1/5 km in 10 seconds. find its initial and final velocity?​

Answer 1

Answer:

Initial velocity = 10 m/s

Final velocity = 30 m/s

Explanation:

As per the provided information in the given question, we have :

• Acceleration (a) = 2m/s²
• Distance (s) = 1/5 km
• Time (t) = 10 seconds

We are asked to calculate initial velocity (u) and final velocity (v).

Let us first convert distance into its Standard form.

$\\ \longrightarrow \sf{\quad {s = \dfrac{1}{5} \; km }}$

• 1 km = 1000 m

$\\ \longrightarrow \sf{\quad {s =\Bigg ( \dfrac{1}{5} \times 1000 \Bigg ) \; m }}$

$\\ \longrightarrow \bf{\quad\underline {s = 200 \; m }}$

★ Calculating initial velocity :

By using the second equation of motion,

$\\ \longrightarrow \quad \pmb{\boxed{\sf {s = ut + \dfrac{1}{2}at^2 }} }$

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

Substitute the values, we have :

$\\ \longrightarrow \sf{\quad {200 = u(10) + \Bigg \lgroup \dfrac{1}{2} \times 2 \times (10)^2 \Bigg \rgroup }}$

$\\ \longrightarrow \sf{\quad {200 = 10u + \lgroup 1 \times 100 \rgroup }}$

$\\ \longrightarrow \sf{\quad {200 = 10u + 100 }}$

$\\ \longrightarrow \sf{\quad {200 -100= 10u }}$

$\\ \longrightarrow \sf{\quad {100= 10u }}$

$\\ \longrightarrow \sf{\quad {\cancel{\dfrac{100}{10}}= u }}$

$\\ \longrightarrow \sf{\quad { 10 = u}}$

$\\ \longrightarrow \bf{\quad\underline { Initial\; velocity= 10 \; m/s}}$

Therefore, initial velocity of the body is 10 m/s.

★ Calculating final velocity (v) :

By using the first equation of motion,

$\\ \longrightarrow \quad \pmb{\boxed{\sf {v = u + at}} }$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time

We found the value of initial velocity above. Substituting all the values we have,

$\\ \longrightarrow \sf{\quad { v = 10 + 2(10)}}$

$\\ \longrightarrow \sf{\quad { v = 10 + 20}}$

$\\ \longrightarrow \sf{\quad { v = 30}}$

$\\ \longrightarrow \bf{\quad\underline { Final \; velocity= 30 \; m/s}}$

Therefore, final velocity of the body is 30 m/s.

More Information :

Equations of motion :

$\boxed{ \begin{array}{cc} \pmb{\sf{ \quad \: v = u + at \quad}} \\ \\ \pmb{\sf{ \quad \: s= ut + \cfrac{1}{2}a{t}^{2} \quad \: } } \\ \\ \pmb{\sf{ \quad \: {v}^{2} - {u}^{2} = 2as \quad \:}}\end{array}}$

• v denotes final velocity
• u denotes initial velocity
• t denotes time
• a denotes acceleration
• s denotes distance