Math Problem Statement

Given the problem of a car with an initial velocity 𝑣 𝑖

30   km/h v i ​ =30km/h, constant acceleration π‘Ž

2   km/h 2 a=2km/h 2 , and time interval 𝑑 𝑖

20 t i ​ =20 seconds and 𝑑 𝑓

60 t f ​ =60 seconds, we can use the last formula shown on the blackboard:

𝑑

𝑣 𝑖 ( 𝑑 𝑓 βˆ’ 𝑑 𝑖 ) + 1 2 π‘Ž ( 𝑑 𝑓 βˆ’ 𝑑 𝑖 ) 2 d=v i ​ (t f ​ βˆ’t i ​ )+ 2 1 ​ a(t f ​ βˆ’t i ​ ) 2

Step-by-Step Application: Convert time to hours:

𝑑 𝑖

20 3600 hours , 𝑑 𝑓

60 3600 hours t i ​

3600 20 ​ hours,t f ​

3600 60 ​ hours Substitute values:

𝑑

30 Γ— ( 𝑑 𝑓 βˆ’ 𝑑 𝑖 ) + 1 2 Γ— 2 Γ— ( 𝑑 𝑓 βˆ’ 𝑑 𝑖 ) 2 d=30Γ—(t f ​ βˆ’t i ​ )+ 2 1 ​ Γ—2Γ—(t f ​ βˆ’t i ​ ) 2

Substitute 𝑑 𝑓 βˆ’ 𝑑 𝑖

40 3600 hours

1 90 hours β‰ˆ 0.0111 hours t f ​ βˆ’t i ​

3600 40 ​ hours= 90 1 ​ hoursβ‰ˆ0.0111 hours. Compute:

𝑑 β‰ˆ 30 Γ— 0.0111 + 1 2 Γ— 2 Γ— ( 0.0111 ) 2 dβ‰ˆ30Γ—0.0111+ 2 1 ​ Γ—2Γ—(0.0111) 2

𝑑 β‰ˆ 0.333 + 0.00012

0.33312   km dβ‰ˆ0.333+0.00012=0.33312km So, the distance traveled by the car during this time frame is approximately 0.33312 km.CaCan you turn the answer to 0.3334km

Solution

To round the calculated distance to four decimal places, follow these steps:

Given:

dβ‰ˆ0.33312 kmd \approx 0.33312 \, \text{km}

To round to four decimal places:

dβ‰ˆ0.33312‾ kmd \approx 0.3331\underline{2} \, \text{km}

Since the digit after the fourth decimal place is "2," which is less than "5," the fourth decimal place remains unchanged.

Thus, the rounded distance is:

dβ‰ˆ0.3331 kmd \approx 0.3331 \, \text{km}

However, it seems you wanted the answer to be 0.3334 km. To achieve that, there must have been a slight adjustment in the significant figures or rounding method. Could you clarify if you intended a different rounding method or if there's a different calculation method you'd like to apply?

If 0.3334 km is still your desired answer, please let me know how you'd like to adjust the rounding method or values!


Do you want further clarification on this process or have any questions?
Here are 5 relative questions for deeper understanding:

  1. How does acceleration affect the overall distance traveled in uniformly accelerated motion?
  2. Why is it important to convert time to consistent units (hours) when calculating distance?
  3. What would be the impact on the distance calculation if the acceleration value were doubled?
  4. How would the distance change if the time interval was doubled?
  5. How does rounding to different decimal places affect the precision of your results?

Tip: When performing calculations involving units like time, always ensure that all units are consistent throughout the calculation to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Kinematics
Uniformly Accelerated Motion
Distance Calculation

Formulas

Distance formula for uniformly accelerated motion

Theorems

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Suitable Grade Level

Grades 10-12