Question

Two cars, A and B, travel in a straight line. The distance of A from the starting point is given

as a function of time by 𝑥𝐴(𝑡) = (2.60 𝑚 / s) 𝑡 + (1.20𝑚 /

𝑠²) 𝑡². The distance of B from the starting point is

𝑥𝐵(𝑡) = (2.80𝑚/𝑠²) 𝑡² − (0.20 𝑚/s³)t³ .

(a) Which car is ahead just after they leave the starting point?

(b) At what time(s) are the cars at the same point?

(c) At what time(s) is the distance from A

to B neither increasing nor decreasing?

(d) At what time(s) do A and B have the same

acceleration?

Answer 1

a)

$$v_{a0}=2.6\frac{m}{a}\\v_{b0}=0\frac{m}{a}$$

Car A is ahead just after they leave the starting point

b)

$$0.2t^2-1.6t+2.6=0\\t_1=0\ s\\t_2=2.27\ s\\t_3=5.73\ s$$

c)

$$0.6t^2-3.2t+2.6=0\\t_1=1\ s\\t_2=4.33\ s$$

d)

$$t=\frac{2.8-1.2}{3(0.2)}=2.67\ s$$