# Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the value x when t = 0 s and asymptote of this function as t → ∞

The equation for the instantaneous position of a car as a function of time, x(t), is derived from its average velocity. The equation can be written in terms of t, which is equal to the number of seconds elapsed since the start.

x(t) = (Initial Position) + [(Average Velocity)(Time)]
= 0 + (28 m/s)(t)
= 28 t m/s

## Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the value x when t = 0 s and asymptote of this function as t → ∞

As t→∞ , the position x approaches infinity and thus this equation has an asymptote at infinity. The value of x when t=0 s is 0 since it is assumed that the initial position of the car was at 0 m. Therefore, when t=0 s, x(t)=0 m or zero meters. This means that when t=0 s, there has been no displacement and hence no distance travelled by the car yet.

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