if a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation.

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14-11-2022
Physics

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if a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation.

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contexto1025 contexto1025 · Answer 1 · 2022-11-18T12:17:21-05:00

Using the concepts of momentum, we got that 13m/sec is the velocity of the ball after 2 sec if the distance the ball has rolled after t seconds is given by s(t) = 5t + 2t2 equation.

Velocity is defined as the derivative of displacement with respect to time

v= ds/dt

The given equation of distance is

s(t) = 5t + 2t² : distance that the ball has rolled after t seconds

v= 4 m/s : initial velocity

t= 2 s

Problem development

s(t) = 5t + 2t²

Using differentiability

v= ds/dt= 5 + 4t : velocity of the ball in function of the time

We replace t =2 s in the equation of velocity

v= 5 + 4(2)

=>v=5+8

=>v=13m/sec.

Hence, if a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, and the distance it has rolled after t seconds is given by the following equation s(t) = 5t + 2t2,then the velocity of the ball after 2 sec is 13m/sec.

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(Complete question) is:

If a ball is given a push so that it has an initial velocity of 4 m/s down a certain inclined plane, then the distance it has rolled after t seconds is given by the following equation. s(t) = 5t + 2t2 . Find the velocity after 2 seconds.