Question

a car, initially traveling 120 ft/s steadily slows to a stop. determine all unknowns and answer the following question.
( s_i = 120 ) ft/s
( \bar{s} = 60 ) ft/s
( s_f = 0 ) ft/s
( d = 240 ) ft
( t = 4 ) s
how far did the car travel during this time?
( 240 ) ft

Explanation:

Step1: Identify the formula for distance

For an object with constant acceleration (or in this case, steady slowing, which is constant deceleration), the distance traveled can be found using the average velocity formula. The average velocity \( v_{avg} \) is the average of the initial velocity \( s_i \) and final velocity \( s_f \), and distance \( d = v_{avg} \times t \).
The initial velocity \( s_i = 120 \, \text{ft/s} \), final velocity \( s_f = 0 \, \text{ft/s} \), and time \( t = 4 \, \text{s} \).
First, calculate the average velocity: \( v_{avg}=\frac{s_i + s_f}{2}=\frac{120 + 0}{2}=60 \, \text{ft/s} \)

Step2: Calculate the distance

Using the formula \( d=v_{avg}\times t \), substitute \( v_{avg} = 60 \, \text{ft/s} \) and \( t = 4 \, \text{s} \).
\( d = 60\times4 = 240 \, \text{ft} \)

Answer:

The car traveled a distance of \(\boldsymbol{240}\) feet.