The position function of a particle is given by:
The velocity function is the derivative of the position:
The particle will be at rest when the velocity is 0, thus we solve the equation:
The coefficients of this equation are: a = 2, b = -9, c = -18
Solve by using the formula:
Substituting:
We have two possible answers:
We only accept the positive answer because the time cannot be negative.
Now calculate the position for t = 6:
Product of polynomials can be done by distribution of multiplication over addition. The product of is
Suppose a, b and c are three numbers. Then we have:
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
The product result of the given expression is
It is because when bases are same and there is multiplication, then powers add up, so we have:
Also, we've
where -ve, +ve are sign of operands and result.
That's why
Thus,
The product of is
Learn more about product of polynomials here:
