Question

two cars are racing! car a steadily speeds up from rest to 70mph at the finish line. car b is already moving 45mph at the start and maintains a constant speed for the duration of the race. determine the initial, average and final velocity of each car and select the winner. which car will win the race? dropdown box image shows two cars with start and finish lines, and boxes labeled ( s_i ), ( s ), ( s_f ) (mph) for each car

Explanation:

Step1: Analyze Car A's Velocities

Car A starts from rest, so initial velocity \( s_i = 0 \) mph. It accelerates steadily to 70 mph at the finish, so final velocity \( s_f = 70 \) mph. For uniformly accelerated motion (speeding up steadily), average velocity \( s=\frac{s_i + s_f}{2}=\frac{0 + 70}{2}=35 \) mph.

Step2: Analyze Car B's Velocities

Car B starts moving at 45 mph, so initial velocity \( s_i = 45 \) mph. It maintains constant speed, so final velocity \( s_f = 45 \) mph, and average velocity \( s = 45 \) mph (since constant speed means average speed equals constant speed).

Step3: Compare Average Speeds to Determine Winner

Average speed determines the time taken for the race (since distance \( d = s \times t \), so \( t=\frac{d}{s} \); lower time means winner). Car A's average speed is 35 mph, Car B's is 45 mph. Since 45 > 35, Car B takes less time.

Answer:

Car B