Question

Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the value x when t=0s.use the given data for the time to reach 400m to calculate a constant of interaction c

Formula:

V(t) =A(1-e^-t/tmax)

Numbers =

t(400m) (s) =10.5

Tmax=7.1s

Answer 1

$v=A(1-e^\frac{t}{tmax})$

$x=\smallint vdx=A\smallint 1-e\frac{-t}{tmax}dt$

$=A[t+tmax×e^\frac{-t}{tmax}]+C$

$400=A[10.5+7.1e^\frac{-10.5}{7.1}]+C$

$C=400-A(12.12)$

$$X=A[t+tmax×e^\frac{-t}{tmax}]+400-12.12A$$

$$X=A[t+tmax×e^\frac{-t}{tmax}-12.12]+400$$

At t=0

$X=A[0+7.1-12.12]+400$

$=400-5.02A$

$=394.98A$ is the answer.