Answer to Question #101014 in Calculus for Leo

Question

Using the mathematical model: to calculate velocity of a car accelerating from rest in straight line. Equation is v(t) = A (1-e ^ -t/t max speed) the ^ means to the power of. v(t) is the instantaneous velocity of the car (m/s), t is the time in seconds, tmaxspeed is the time to reach the maximum speed in seconds and A is a constant. We are given the information that the car has a t(0-28m/s) of 2.6s, a t(400m) of 10.46s, and a tmaxspeed of 7s (S stands for seconds in this instance) 1. Identify the units of the coefficient A, 2. physical meaning of A, 3. velocity of the car at t=0 and 4. asymptote of this function as t ⮕ ∞?

Answer 1

$v(t)=A(1-e^{-t/t_o})$

$A=constant$

$t=time$ (in seconds)

$t_o=$ time to reach the maximum speed

$t_o=7s$

1.The coefficient A has a unit same as the velocity, that is, m/s.

2.Terminal Velocity(as t tends to infinity, velocity tends to A)

3.$v(t)=A(1-e^{-t/t_o})$

$A(1-e^{-(2.6/7)})=-28$

$A(0.31)=-28$

$A=-28/0.31=-90.322m/s$

$v(0)=A(1-1)=0m/s$

4.As t tends to infinity,v(t) tends to the terminal velocity equal to A.

The asymptote of this function is $y=-90.322$ .