2 race cars start from the same position with 0 velocity. Car A accelerates with 3.50 m/s^2, car B accelerates with 4.9 m/s^2 with a 1.00 second delay. how long will it take for car B to reach car A?

Answer 1

In these types of questions, always ask yourself, "What's the same for both cars?" In this case, the distance they travel is the same. So, we'll apply the equation Δx = v_ot + 1/2at². Both cars start from rest, so it reduces to Δx = 1/2at². They have the same distance, but different accelerations and different times. So, Δx_A = 1/2a_At_A² = Δx_B = 1/2a_Bt_B². Set 1/2a_At_A² = 1/2a_Bt_B². Dividing both sides by 1/2 and substituting accelerations, 3.5t_A²=4.9t_B². Car B is moving for 1 second less than Car A, so t_B=t_A-1. Let t = t_A, 3.5t² = 4.9(t-1)². I can use algebra to solve for t: divide both sides by 4.9, so 0.714t²=(t-1)², take the square root of both sides, so 0.845t=t-1, 1=0.155t, t=6.45s or t=6.458s if you don't round until the end. Alternatively, I can graph both equations for Δx and find the intersection, arriving at the same answer, t=6.458s.