Physics, asked by pandeyankitgmailcom, 1 year ago

At t=0 , a body starts from origin with some initial velocity. the displacement x in m of the body varies with time in s as x= -2/3t sqr + 16t +2. find the initial velocity of the body and also find how long does the body come to rest. what is the acceleration of the body when it come to rest.

Answers

Answered by santy2
1

Velocity = Δ in Displacement with time

Acceleration = Δ in velocity with time

Since in this case we are given a displacement function, we get the velocity and acceleration by differentiating x with respect to time.

For velocity we take the first derivative.

For acceleration we take the second derivative.

Velocity

Dx/dt of x = - 2/3t² + 16t + 2

V = - 4/3t + 16

Acceleration

= d²x/dt²

= - 4/3

Initial velocity

At the start point t = 0

Initial velocity = - 4/3 × 0 + 16

= 16m/s

The time taken by the body to come to rest.

At rest the velocity = 0

Hence :

-4/3t + 16 = 0

-4/3t = - 16

-4t = - 48

t = 48/4

t = 12 seconds

Acceleration = - 4/3 m/s²

The negative sign indicates that the body is decelerating.

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