Answer to Question #89979 in Mechanics | Relativity for brittany

Question

You and your friend decide to get into your cars and begin to race. From previous experience, you know that your friend’s car has an acceleration of 3.25 m/s2 and your car has an acceleration of 4.15 m/s2, so you decide to wait to start 3.0 s after your friend leaves the starting line. a) How long does it take for you to catch up to your friend? b) how fast are you and your friend going at the time you catch up to them. c) How far did you need to travel before you caught up with your friend?

Answer 1

a)

$$0.5a_1 (t+t_0)^2=0.5a_2t^2$$

$$3.25(t+3)^2=4.15t^2$$

$$t=23\ s$$

b)

$$v_1=a_1(t+t_0)=3.25(23+3)=84.5 \frac{m}{s}$$

$$v_2=a_2 t=4.15(23)=95.5 \frac{m}{s}$$

c)

$$d=0.5a_2t^2=0.5(4.15)(23)^2=1100\ m$$