Question

a particle start from a point from a velocity of 6 m/sand moves with an acceleration of -2m/second square.show that after 6 sec the particle will be at starting point

Answer 1

Given

A particle starts from a point from a velocity of 6m/s with an acceleration of -2 m/s² .

To show

After 6 seconds, the particle will be at starting point.

Solution

As here we have to show that the particle will be in its initial point, so if we get distance crossed = 0 then it will showed that the particle will be in its initial point.

As we know equation of kinematics :

☛ s = ut + ½ at²

Putting values :

⇒ s = (6 × 6) + ½ (-2 × 6²)

⇒ s = 36 + ½ (-2 × 36)

⇒ s = 36 + ½ (-72)

⇒ s = 36 - 36

⇒ s = 0

That means, particle will come back to its initial point as its distance crossed = 0 , so the particle's distance is 0.

Therefore,

After 6 seconds,the particle will be in its initial point. [Showed]

Answer 2

Given:-

A particle starts from a point with  velocity of 6 m/s and acceleration -2 m/s².

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To prove:-

After 6 sec the particle will be at starting point.

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Proof:-

• v = 0 m/s

• u = 6 m/s

• a = -2 m/s²

• t = 6 s

We know,

$\bold{s=ut+\frac{1}{2}at^2 }\\\\\bold{\implies s=6*6+\frac{1}{2}(-2)6^2 }\\\\\bold{\implies s=36+(-1*36)}\\\\\bold{\implies s=36-36=0}\\\\\text{We know, that distance can never be 0, but displacement can be 0 if}\\\text{the object again comes to its initial point back. So, we can prove here}\\\text{that the particle finally reached to its starting point after a time gap of }\\\text{6 seconds.}$

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Proved.