Question

two cars are racing! car a steadily speeds up from rest to 50mph at the finish line. car b is already moving 15mph 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 with yellow box image with two cars, start/finish lines, boxes for s_i, s, s_f

Explanation:

Step1: Analyze Car A's velocities

Car A starts from rest, so initial velocity \( s_i = 0 \) mph. It speeds up steadily (uniformly accelerated motion) to 50 mph at the finish, so final velocity \( s_f = 50 \) mph. For uniform acceleration from rest, average velocity \( \bar{s} = \frac{s_i + s_f}{2}=\frac{0 + 50}{2}=25 \) mph.

Step2: Analyze Car B's velocities

Car B starts moving at 15 mph, so initial velocity \( s_i = 15 \) mph. It maintains constant speed, so final velocity \( s_f = 15 \) mph, and average velocity \( \bar{s}=15 \) mph (since constant speed means average = instantaneous speed).

Step3: Compare average velocities

Average velocity determines the distance covered in time \( t \) (distance \( d=\bar{s} \times t \)). Car A's average velocity (25 mph) is greater than Car B's (15 mph). So in the same race distance, Car A takes less time (\( t=\frac{d}{\bar{s}} \), smaller \( \bar{s} \) would take more time, but here A has larger \( \bar{s} \), so less time).

Answer:

For Car A:

• Initial velocity (\( s_i \)): \( 0 \) mph
• Average velocity (\( \bar{s} \)): \( 25 \) mph
• Final velocity (\( s_f \)): \( 50 \) mph

For Car B:

• Initial velocity (\( s_i \)): \( 15 \) mph
• Average velocity (\( \bar{s} \)): \( 15 \) mph
• Final velocity (\( s_f \)): \( 15 \) mph

Winner: Car A