Question

If y(t)y(t) describes the position with time, what is the proper formula for velocity with time? (Recall velocity is related to the derivative of position with time.)

Answer 1

Answer:

Although this question is not complete, I would give a general solution to this kind of problems.

If y(t) describes the position of a body with time such that

y(t) = at^(n) + bt^(m) + C

Then

V(t) = dy(t)/dt = ant^(n-1) + bmt^(m-1)

Explanation:

As an example supplies the position of a particle is given by

y(t) = 4t³- 3t² + 9

V(t) = 4x3t²- 3x2t¹

V(t) = d(t)/dt = 12t² - 6t.

Another example,

If y(t) = 15t³ - 2t² + 30t -80

V(t) = d(t)/dt = 15x3t² - 4t +30 = 45t² + 4t + 30.

Basically, in the equations above the powers of t reduces by one when computing the velocity function from y(t) by differentiation (calculating the derivative of y(t)). The constant term C (9 and 80 in the functions of y(t) in examples 1and 2 above) reduces to zero because the derivative of a constant (and ordinary number without the t attached to it) is always zero.

One last example,

y(t) = 2t^6 -3t²

V(t) = d(t)/dt = 12t^5 - 6t