Question

a boy starting from rest runs with a uniform acceleration for 5 sec such that he covers a distance of 37.5m in 5 sec calculate the acceleration of the boy and final velocity of the body​

Answer 1

Answer:

a = 3 m/s²

v = 15 m/s

Explanation:

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

• Initial velocity (u) = 0 m/s [Starts from rest]
• Time taken (t) = 5 seconds
• Distance (s) = 37.5 m

We've been asked to calculate the acceleration and the final velocity of the body.

Acceleration is defined as the rate of change in velocity. Its SI unit is m/s². It is a vector quantity. We can find the acceleration using the second equation of motion. By using the second equation of motion:

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

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

Substitute the values.

$\longrightarrow \sf{\quad { 37.5 = 0(5) + \dfrac{1}{2}\times a \times (5)^2}}$

$\longrightarrow \sf{\quad { 37.5 = \dfrac{1}{2}\times a \times 25}}$

$\longrightarrow \sf{\quad { 37.5 \times 2= 1 \times a \times 25}}$

$\longrightarrow \sf{\quad { 75= 25a}}$

$\longrightarrow \sf{\quad { \cancel{\dfrac{75}{25}}= a}}$

$\longrightarrow \quad\underline{\boxed {\pmb{\frak{3 \; m \: s}}^{\pmb{\frak{-2}}}=\pmb{\frak{ a}}}}$

Therefore, acceleration is 3 m/s².

Now, we have to find the final velocity of the body. In order to find that so, we'll use the first equation of motion :

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

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

Substitute the values.

$\longrightarrow \sf{\quad { v = 0 + 3(5)}}$

$\longrightarrow \quad\underline{\boxed {\pmb{\frak{ v }} = \pmb{\frak{15 \; m \: s}}^{\pmb{\frak{-1}}}}}$

Therefore, final velocity of the body is 15 m/s.

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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
• a denotes acceleration
• t denotes time
• s denotes distance