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Class 10 Class 12
A particle starts with a velocity of 200 cm/s and moves in a straight line with a retardation of 10 cm/s2. Find the time it takes to describe 1500 cm and explain the double answers.

Here, we have

Initial velocity, u = 200 cm/s

Acceleration, a = -10 cm/s2

Distance travelled, s = 1500 cm

Time taken, t = ?

Using the relation,

s = ut + 1/2 at2

1500 = 200 t + 1/2(-10)t2

On solving the equation,we get

t = 10 s or t = 30 s

Here, the value of 10 s corresponds to the time when the particle first arrives at the given location. It then crosses this point and at the end of 20 s, its velocity is just 0.

The particle then returns and at the end of 10 s more, is again at the given location from the starting point.

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What is a scalar quantity?

A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
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Give three examples of scalar quantities.

Mass, temperature and energy
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Give three examples of vector quantities.

Force, impulse and momentum.
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What is a vector quantity?

A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
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What are the basic characteristics that a quantity must possess so that it may be a vector quantity?

A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.

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