Question

a tuck starts from rest and rolls down a hill with a constant acceleration if travels a distance of 400mt in 20 seconds find its acceleration . find the force acting on it , if it's mass is 7 tonnes (1 tonne is equal to 1000kg )​

Answer 1

${\large{\underline{\pmb{\sf{Given...}}}}}$

★ A tuck starts from rest and rolls down a hill with a constant acceleration

★ it travels a distance of 400m in 20 seconds

★ the mass of the truck is 7 tonnes

${\large{\underline{\pmb{\sf{To\;Find...}}}}}$

★ The acceleration of the truck

★ The force acting on the truck

${\large{\underline{\pmb{\sf{Understanding \; the \; question...}}}}}$

❍ Concept : As we have been said that the truck starts form rest [ it's initial velocity ] with a constant acceleration and the distance travelled which is 400 m in 20 seconds and said that the mass of the truck is 7 tonnes.

★ So let's use suitable formulae in both the cases of finding the acceleration of the truck and the amount force acting upon the truck using the given statements.

${\large{\underline{\pmb{\sf{Using\; concepts...}}}}}$

✪ Formula to find the acceleration of an object :

$\tt S = ut + \dfrac{1}{2} at^{2}$

✪ Formula to find the force :

$\tt Force = Mass\times Acceleration$

${\large{\underline{\pmb{\sf{ Solution...}}}}}$

★ The acceleration of the truck is 2m/s^2 and the force acting upon the truck is 14,000N  

${\large{\underline{\pmb{\sf{Full\; Solution...}}}}}$

★ Firstly let's find the acceleration of the truck

→ Formula :

$\tt S = ut + \dfrac{1}{2} at^{2}$

→ Where,

• S denotes the distance
• u denotes initial velocity
• t denotes time
• a denotes acceleration

→ Here,

• S = 400m
• u = 0m/s^2
• t = 20 s

~ Now let' substitute the values in the above mentioned formulae and find the required solution .

➟ S = ut + 1/2 × a × t × t

➟ 400 = 0 × 20 + 1/2 × a  × 20 × 20

➟ 400 = 0 × 20 + 1/2 × 400a

➟ 400 = 0 × 20 + 200a

➟ 400 = 0 + 200a

➟ 400 = 200a

➟ a = 400/200

➟ a = 2m/s^2

• Henceforth the acceleration of the truck is 2m/s^2

~As we have found the acceleration now, let's find the force acting upon the truck.

→ Formula :

$\tt Force = Mass \times Acceleration$.

→ Here,

• Mass = 7 tonnes
• Acceleration = 2m/s^2

~ As we know that when we evaluate something we'll have to make sure that they belong to the same unit. now as the mass in the unit of tonnes let's convert it into S.I system ( kilograms )

${\bf{\red{ hint : }}}$ 1 ton = 1000 kg

★ So, 7 tonnes = 7 × 1000kg = 7000kg

~Now, let;s substitute the values in the formula and find the force acting upon.

➟ F = M × A

➟ F = 7000 × 2

➟ F = 14000N

• Henceforth the force acting upon the truck is 14000 newton

${\underline{\large{\pmb{\sf{Additional \; Info...}}}}}$

${\underline{\underline{\sf{\bigstar{Other \; formula \; to\; find \; acceleration :}}}}}$

✪ Formula :

$\tt a = \dfrac{u-v}{t}$

${\underline{\underline{\sf{\bigstar{Other \; formula \; to\; find \; force :}}}}}$

✪ Formula :

$\tt Force = Pressure \times Area$

${\underline{\underline{\sf{\bigstar{Newton's \; law \; of \; gravitation :}}}}}$

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Answer 2

Answer:

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