Question

An object moving with a velocity of 90 km/h reduce it's velocity to 72km/h in 2 sec find its acceleration​

Answer 1

Provided that:

• Initial velocity = 90 km/h
• Final velocity = 72 km/h
• Time taken = 2 seconds

To calculate:

• Acceleration

Solution:

• Acceleration = -2.5 m/s²

Using concepts:

• Formula to convert km/h into m/s

• Acceleration formula

Using formula:

• ${\small{\underline{\boxed{\sf{a \: = \dfrac{v-u}{t}}}}}}$

(Where, a denotes acceleration, v denotes final velocity, u denotes initial velocity and t denotes time taken)

Required solution:

~ Firstly let us convert km/h into m/s

Converting 90 km/h into m/s

$:\implies \sf 90 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{90} \times \dfrac{5}{\cancel{{18}}} \\ \\ :\implies \sf 5 \times 5 \\ \\ :\implies \sf 25 \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

Converting 72 km/h into m/s

$:\implies \sf 72 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{72} \times \dfrac{5}{\cancel{{18}}} \\ \\ :\implies \sf 4 \times 5 \\ \\ :\implies \sf 20 \: ms^{-1} \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

Therefore,

• Initial velocity = 25 m/s
• Final velocity = 20 m/s

Dear web users, you can see step of cancelling from 1st and 2nd attachment(s)

~ Now let's calculate acceleration!

$:\implies \sf Acceleration \: = \dfrac{Change \: in \: velocity}{Time} \\ \\ :\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20-25}{2} \\ \\ :\implies \sf a \: = \dfrac{-5}{2} \\ \\ :\implies \sf a \: = -2.5 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = -2.5 \: ms^{-2} \\ \\ :\implies \sf Retardation \: = -2.5 \: ms^{-2} \\ \\ {\pmb{\sf{Therefore, \: solved!}}}$

Knowledge booster:

$\begin{gathered}\boxed{\begin{array}{c}\\ \bf What \: is \: acceleration? \\ \\ \sf The \: rate \: of \: change \: of \: velocity \: of \: an \\ \sf object \: with \: respect \: to \: time \\ \sf is \: known \: as \: acceleration. \\ \\ \sf \star \: Negative \: acceleration is \: known \: as \: deacceleration. \\ \sf \star \: Deacceleration \: is \: known \: as \: retardation. \\ \sf \star \: It's \: SI \: unit \: is \: ms^{-2} \: or \: m/s^2 \\ \sf \star \: It \: may \: be \: \pm ve \: or \: 0 \: too \\ \sf \star \: It \: is \: a \: vector \: quantity \\ \\ \bf Conditions \: of \pm ve \: or \: 0 \: acceleration \\ \\ \sf \odot \: Positive \: acceleration: \: \sf When \: \bf{u} \: \sf is \: lower \: than \: \bf{v} \\ \sf \odot \: Negative \: acceleration: \: \sf When \: \bf{v} \: \sf is \: lower \: than \: \bf{u} \\ \sf \odot \: Zero \: acceleration: \: \sf When \: \bf{v} \: \sf and \: \bf{u} \: \sf are \: equal \end{array}}\end{gathered}$