Math Problem Statement
Solution
Let's break down and solve the problem presented in the image. The question is in Indonesian, and it can be translated as follows:
Problem:
A car is moving in a straight line with an initial velocity of 36 km/h. After covering a distance of 150 meters, the speed becomes 72 km/h.
A. What is the acceleration experienced by the car?
B. What is the time taken by the car to travel the distance?
C. Create a GUI based on the answers to this problem.
D. Write a program that matches the GUI created.
Let's solve parts A and B first.
Part A: Find the acceleration experienced by the car.
- Initial velocity (u): 36 km/h =
- Final velocity (v): 72 km/h =
- Distance (s): 150 m
To find the acceleration , we can use the equation of motion:
Rearranging to find :
Substitute the values:
Part B: Find the time taken by the car.
We can use the following kinematic equation to find the time :
Rearrange to find :
Let me calculate these now.### Part A: The acceleration experienced by the car is 1 m/s².
Part B:
The time taken by the car to travel the distance of 150 meters is 10 seconds.
Would you like more details on how these were calculated, or guidance on parts C and D regarding the GUI and program?
Here are 5 related questions that might deepen your understanding:
- How can we derive other kinematic equations from the basic principles of motion?
- What if the initial or final velocity was different—how would that affect the acceleration?
- Can we calculate the car’s motion under a non-uniform acceleration?
- What happens if there is resistance, like friction, acting on the car?
- How would the calculation change if we measured velocity in meters per second from the start?
Tip: When converting units like km/h to m/s, always remember to divide by 3.6.
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Math Problem Analysis
Mathematical Concepts
Kinematics
Acceleration
Equations of Motion
Formulas
v^2 = u^2 + 2as
v = u + at
Theorems
Equations of motion for uniformly accelerated motion
Suitable Grade Level
High School (Grades 10-12)
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