Question

a motor cycle travelling at 32km/h increases its velocity uniformily to 74 km/h in the time of 3 sec.its acceleration in m/sec^2 is

Answer 1

$\large \underline{\textbf{Given That}}$

$\textsf{A motor cycle increased its velocity from \bf{32km/h \: to \:74km/h\: in\: 3\: seconds.}}$

$\sf{Now \:we \:need\: to\: find\: it's\: acceleration\: in\: m/{s}^{2}}$

$\large \underline{\textbf{Answer}}$

$\sf{Now \: according \: to \: question}$

$\bf{Initial\: Velocity\:( u )\: = 32km/h}$

$\bf{Final\: Velocity\:( v )\: = 74km/h}$

$\bf{And\: Time \: = \: 3s}$

$\boxed{\bf{\bigstar\quad Acceleration \:= \: \dfrac{Change\: in\: velocity }{Time}\quad \bigstar}}$

$\sf{As \:per \:Question \:we\: need \:to\: find \:Acceleration\: in\: m/s^2}$

$\textsf{For that we need to convert Final and Initial velocities into m/s }$

$\underline{\textsf{Converting Velocities into m/s}}$

$\sf{Initial \:velocity\: = \:32km/h \:\times \:5/18 \implies \: 8.89\:m/s (approx) }$

$\sf{Final \:velocity\: = \:74km/h \:\times \:5/18 \implies \: 20.56 \:m/s (approx) }$

$\textsf{\bf{Change In Velocity = Final velocity - Initial velocity }}$

$\sf{\therefore \: We \: Have \implies}$

$\mathbf{Acceleration\:=\dfrac{20.56\:-\:8.89}{3s}}$

$\mathbf{ Acceleration \: = \:3.89\: m/s^2}$

$\underline{\textbf{Hence The Required Answer Is}}$

$\boxed{\boxed{\mathbf{3.89 \:m/s^2}}}$

$\underline{\bf{Points\: To\: Be\: Remembered}}$

$\textbf{Initial velocity}$ - Velocity that an object has at initial time of reference ( As per Question )

$\textbf{Final velocity}$- Velocity that an object has at initial time of reference

[Here we used $\mathbf{5/18 \:as\: to \:convert\; km/h\: to \:m/s}$ .In actual sense 5/18 is just the simplified form of -

$\mathbf{1km/hr\:= \:\dfrac{1000}{1} \times 60 \times 60\: =\: \dfrac{1000}{3600}\: =\:\dfrac{5}{18}\:m/s}$