Question

The displacement x of a particle varies with time t as x=-5t2+20t+30. Find the position,velocity , acceleration of the particle at t=0.when will the velocity of the particle become 0?

Answer 1

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Answer 2

Explanation:

Let us assume SI units are to be used

position x = ( -5t² + 20t + 30 )

Velocity dx/dt = (-5t + 20) m/s

To find acceration differentiate equation of velocity w.r.t t,

We get d^2 x/dt^2 = -5.

Thus, acceleration = -5 m/s²

Since acceleration is constant, this motion is uniformly accelerated motion.

Velocity will become zero when t = 20/5 = 4 seconds.

Now,

Position =  -5(4)² + 20(4) + 30 = -80 + 60 + 30 = 10 m

Therefore,

Position = 10 m

Velocity will become 0 in 4 seconds.

Acceleration = -5 m/s²

Hope it helps!