Question

two cars are racing! car a steadily speeds up from rest to 60mph at the finish line. car b is already moving 40mph 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? * car b

Explanation:

Step1: Analyze Car A's velocities

Car A starts from rest, so initial velocity \( s_i = 0 \) mph. It accelerates steadily to 60 mph, so final velocity \( s_f = 60 \) mph. For uniformly accelerated motion (speeding up steadily), average velocity \( s=\frac{s_i + s_f}{2}=\frac{0 + 60}{2}=30 \) mph.

Step2: Analyze Car B's velocities

Car B starts with 40 mph and maintains constant speed, so initial \( s_i = 40 \) mph, average \( s = 40 \) mph, final \( s_f = 40 \) mph.

Step3: Compare average velocities

Since average velocity determines distance covered in time (\( d = s\times t \)), Car B has higher average velocity (40 mph > 30 mph) for same race duration, so it wins.

Answer:

Car B will win the race. For Car A: Initial velocity \( s_i = 0 \) mph, Average velocity \( s = 30 \) mph, Final velocity \( s_f = 60 \) mph. For Car B: Initial velocity \( s_i = 40 \) mph, Average velocity \( s = 40 \) mph, Final velocity \( s_f = 40 \) mph.