Question

The horizontal position of an object varies with time according to this expression: x(t)=3+5t+9t², where the position is measured in meters and time in seconds.

(a) Write an expression for the x-component of the velocity as a function of time.

Answer 1

The expression for the x-component of the velocity as a function of time is v(t) = 5 + 18t.

Step-by-step explanation:

To find the expression for the x-component of the velocity, we need to take the derivative of the given position expression with respect to time. The derivative of x(t) = 3 + 5t + 9t² is v(t) = 5 + 18t.

So, the expression for the x-component of the velocity as a function of time is v(t) = 5 + 18t.

In theoretical physics, "expression" can be used to describe a more abstract representation of a physical concept or idea. This may involve using mathematical symbols, diagrams, or other forms of notation to capture the essence of a physical phenomenon.