Question

A person is applying a force of 50 Newton on a object with mass 20 kg and the μ is 0.15 with surface . if its initial velocity was 0 , then find final velocity and acceleration for 5 seconds .

[hint :- friction = μmg]​

Answer 1

Solution -

Given -

• Force applied on object (f) = 50 N
• Mass of object (m) = 20 Kg
• μ = 0.15 with surface
• Initial velocity (u) = 0
• Time (t) = 5 sec

$\begin{gathered} \underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\ \end{gathered}$

To Find -

• Final Velocity (v) = ?
• Acceleration (a) = ?

$\begin{gathered} \underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\ \end{gathered}$

Formula -

• $\begin{gathered} \ \sf{\quad {F_{(friction)} = \mu \: mg }} \\ \end{gathered}$
• $\begin{gathered} \sf{\quad {F_{(force)} - {F_{(friction)}} = m_{(mass)} \times a _{(acceleration)} }} \\ \end{gathered}$
• $\begin{gathered} \sf{\quad {v_{(final \: Velocity)} = {u_{(initial \: velocity)}} + a_{(acceleration)} \times t _{(time)} }} \\ \end{gathered}$

$\begin{gathered} \underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\ \end{gathered}$

Solution -

By applying the formula

$\begin{gathered} \sf{\quad {F_{(force)} - {F_{(friction)}} = m_{(mass)} \times a _{(acceleration)} }} \\ \end{gathered}$

• F = 50
• Friction = 0.15×20×10 (gravity = 10)
• m = 20
• a = ?

on substituting the values ,

$\begin{gathered} :\Longrightarrow \sf{\quad {50 - 0.15 \times 20 \times 10 = 20 \times a}} \\ \end{gathered}$

$\begin{gathered} :\Longrightarrow \sf{\quad {50 - 30 = 20 \times a}} \\ \end{gathered}$

$\begin{gathered} :\Longrightarrow \sf{\quad {\dfrac{20}{20} = a} }\\ \end{gathered}$

$\begin{gathered} :\Longrightarrow \sf{\quad {a = 1m/s^{2}} }\\ \end{gathered}$

Hence , Acceleration = 1 m/s²

Now ,

By applying the formula

$\begin{gathered} \sf{\quad {v_{(final \: Velocity)} = {u_{(initial \: velocity)}} + a_{(acceleration)} \times t _{(time)} }} \\ \end{gathered}$

• u = 0
• a = 1
• t = 5

on substituting the values ,

$\begin{gathered} :\Longrightarrow \sf{\quad {v = 0 + 1 \times 5}} \\ \end{gathered}$

$\begin{gathered} :\Longrightarrow \sf{\quad {v = 5 m/s} }\\ \end{gathered}$

Hence , Final Velocity = 5 m/s

Answer 2

• Acceleration = 1 m/s²

• Final Velocity = 5 m/s