Question

A body with an initial velocity of 8 m/s accelerates uniformly at the rate of 9cm/s2. If the distance covered by the body is 200 m, calculate 2M
a) The final velocity
b) the time taken to cover the distance (in SI Units)

Answer 1

ProvidEd that:

• Initial velocity = 8 m/s
• Acceleration = 9 cm/s²
• Distance = 200 m

To calculaTe:

• The final velocity

• Time taken to cover this distance

SoluTion:

• The final velocity = 10 m/s
• Time taken = 22.22 s

KnowlEdge required:

• SI unit of velocity = m/s
• SI unit of time = seconds
• SI unit of acceleration = m/s²
• SI unit of distance = m

UsiNg concepts:

• Formula to convert cm into m
• Third equation of motion
• First equation of motion

UsiNg formulas:

• Formula to convert cm into m:

• ${\small{\underline{\boxed{\pmb{\sf{1 \: cm \: = \dfrac{1}{100} \: m}}}}}}$

• First equation of motion:

• ${\small{\underline{\boxed{\pmb{\sf{v \: = u \: + at}}}}}}$

• Third equation of motion:

• ${\small{\underline{\boxed{\pmb{\sf{v^2 \: - u^2 = \: 2as}}}}}}$

RequirEd solution:

~ Firstly let us convert centimetres into metres!

$:\implies \sf 1 \: cm \: = \dfrac{1}{100} \: m \\ \\ :\implies \sf 9 \: cm \: = \dfrac{9}{100} \: m \\ \\ :\implies \sf 9 \: cm \: = 0.09 \: m \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}$

Therefore,

• Acceleration = 0.09 m/s²

~ Now let's calculate the final velocity by using third equation of motion!

$:\implies \sf v^2 \: - u^2 = \: 2as \\ \\ :\implies \sf v^2 - (8)^{2} = 2(0.09)(200) \\ \\ :\implies \sf v^2 - 64 = 400(0.09) \\ \\ :\implies \sf v^2 - 64 = 36 \\ \\ :\implies \sf v^2 = 36 + 64 \\ \\ :\implies \sf v^2 = 100 \\ \\ :\implies \sf v = \sqrt{100} \\ \\ :\implies \sf v = 10 \: ms^{-1} \\ \\ :\implies \sf Final \: velocity = 10 \: ms^{-1}$

~ Now let's calculate the time taken by using first equation of motion!

$:\implies \sf v \: = u \: + at \\ \\ :\implies \sf 10 \: = 8 + 0.09(t) \\ \\ :\implies \sf 10 \: = 8 + 0.09t \\ \\ :\implies \sf 10 - 8 \: = 0.09t \\ \\ :\implies \sf 2 \: = 0.09t \\ \\ :\implies \sf \dfrac{200}{9} \: = t \\ \\ :\implies \sf 22.22 \: = t \\ \\ :\implies \sf t \: = 22.22 \: seconds \\ \\ :\implies \sf Time \: = 22.22 \: seconds$