Question

a car initially traveling 10ft/s, steadily speeds up to 60ft/s in 7.3s. determine all unknowns and answer the following question.
s_i =
unit
s =
unit
s_f =
unit
d =
unit
t =
unit
how far did the car travel during this time?
unit

Explanation:

Step1: Identify known values

Initial velocity \( s_i = 10 \, \text{ft/s} \), final velocity \( s_f = 60 \, \text{ft/s} \), time \( t = 7.3 \, \text{s} \). We need to find the distance \( d \). For uniformly accelerated motion (steady speeding up, so constant acceleration), the distance can be found using the average velocity formula: \( d=\frac{s_i + s_f}{2}\times t \).

Step2: Calculate average velocity

Average velocity \( v_{avg}=\frac{s_i + s_f}{2}=\frac{10 + 60}{2}=\frac{70}{2} = 35 \, \text{ft/s} \).

Step3: Calculate distance

Using \( d = v_{avg}\times t \), substitute \( v_{avg}=35 \, \text{ft/s} \) and \( t = 7.3 \, \text{s} \). So \( d=35\times7.3 = 255.5 \, \text{ft} \).

For the unknowns:

• \( s_i = 10 \, \text{ft/s} \) (initial speed)
• \( s \) (maybe average speed, which we calculated as 35 ft/s)
• \( s_f = 60 \, \text{ft/s} \) (final speed)
• \( d \) (distance, 255.5 ft)
• \( t = 7.3 \, \text{s} \) (time)

Answer:

• \( s_i = 10 \, \text{ft/s} \)
• \( s = 35 \, \text{ft/s} \)
• \( s_f = 60 \, \text{ft/s} \)
• \( d = 255.5 \, \text{ft} \)
• \( t = 7.3 \, \text{s} \)
• Distance traveled: \( 255.5 \, \text{ft} \)