Answer:
the equation for v is v = 250 km/h * [1- e^(-kt) ]
Step-by-step explanation:
since the acceleration "a" is the rate of change of velocity "v" with respect to the time "t", we have
a= dv/dt= k*(250 - v)
thus
dv / (250 - v) = k*dt
if we proceed then to the indefinite integration in both sides
∫dv / (250 - v) = ∫k*dt
- ln (250-v) = k*t +C , where C= constant
if we know that at t=0 , v(t=0)=0 , then
- ln (250-0) = k*0 +C
- ln 250 = C
replacing C in the original equation:
- ln (250-v) = k*t - ln 250
ln [(250-v)/250] = -k*t
v = 250 km/h * [1- e^(-kt) ]
