1.

A Trucks movie with velocity 36 km per hour and gains its speed to 72 km per hour in 5 seconds. Find the acceleration of the truck.a) 20m/s²b) 2m/s²c) 20m/s²d) 0.20m/s²​

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Answer:

Provided that:

  • Initial velocity = 36 kmph
  • Final velocity = 72 kmph
  • Time = 5 seconds

To calculate:

  • The acceleration

Solution:

  • The acceleration = 2 m/s²

Using concepts:

• We can use either acceleration formula or first EQUATION of motion to calculate the acceleration.

• Formula to CONVERT kmph-mps.

Using FORMULAS:

• Acceleration formula:

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

• First equation of motion:

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

• Formula to convert kmph-mps:

  • {\small{\underline{\boxed{\pmb{\sf{1 \: kmph \: = \dfrac{5}{18} \: mps}}}}}}

Where, a DENOTES acceleration, u denotes initial velocity, v denotes final velocity, t denotes time taken.

Required solution:

~ Firstly let us convert kmph-mps!

Converting 72 kmph-mps.

:\implies \sf 72 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{72} \times \dfrac{5}{\cancel{{18}}} \: (Cancelling) \\ \\ :\implies \sf 4 \times 5 \\ \\ :\implies \sf 20 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}

Converting 36 kmph-mps.

:\implies \sf 36 \times \dfrac{5}{18} \\ \\ :\implies \sf \cancel{36} \times \dfrac{5}{\cancel{{18}}} \: (Cancelling) \\ \\ :\implies \sf 2 \times 5 \\ \\ :\implies \sf 10 \: mps \\ \\ {\pmb{\sf{Henceforth, \: converted!}}}

Therefore,

  • Initial velocity = 10 mps
  • Final velocity = 20 mps

~ Now let's FIND out the acceleration!

By using acceleration formula.

:\implies \sf a \: = \dfrac{v-u}{t} \\ \\ :\implies \sf a \: = \dfrac{20 - 10}{5} \\ \\ :\implies \sf a \: = \dfrac{10}{5} \\ \\ :\implies \sf a \: = 2 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 2 \: ms^{-2}

By using first equation of motion.

:\implies \sf v \: = u \: + at \\ \\ :\implies \sf 20 = 10 + a(5) \\ \\ :\implies \sf 20 - 10 = 5a \\ \\ :\implies \sf 10 = 5a \\ \\ :\implies \sf a \: = \dfrac{10}{5} \\ \\ :\implies \sf a \: = 2 \: ms^{-2} \\ \\ :\implies \sf Acceleration \: = 2 \: ms^{-2}


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