A vehicle accelerates down on ramp and eventually reaches highway speed. The position of the vehicle is described by the following equation:

x(t) = At ² /(t + B)

(a) Write an expression for the vehicle's instantaneous velocity as a function of time.

v(t) = (2At)(-1 (t + B) ^-2 )

Velocity is the rate of change of position. What mathematical operation represents the "rate of change" of a function?

You must take the derivative of one function divided by another function. What rule for derivatives must you use?

(b) What is the initial velocity of the vehicle?

(c) What is the vehicle's velocity after accelerating for 10 seconds? The equation 's parameters are as follows, A = 33 m/s B = 21 s

(d) After accelerating, the velocity of the vehicle will begin to level off at highway speed. Write an expression for the vehicle's velocity after it has been accelerating for a long time.

(e) Determine the value of the vehicle's velocity after it has been accelerating for a long time. The equation's parameters are as follows, A = 33 m/s B = 21 s.

a 0 d j P B A 00x5 g k S B h m t