Aparticle moves in a straight line and has acceleration given by a(t) = 12t + 10. its initial velocity is v(0) = −5 cm/s and its initial displacement is s(0) = 9 cm. find its position function, s(t).

The position function is .

Explanation:

Given that,

Acceleration

Initial velocity

Initial displacement

We know that,

The acceleration is the rate of change of velocity of the particle.

The velocity is the rate of change of position of the particle

We need to calculate the the position

The acceleration is

On integration both side

At t = 0

Now, On integration again both side

At t = 0

Hence, The position function is .

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.