Math Problem Statement
Solve it
Solution
The problem asks to calculate the speed of the fighter jet just before it decelerates to a complete stop after covering a distance of 44.2 m, knowing that it initially stopped after traveling 197.4 m at a speed of 70.4 m/s.
We can approach this using the equation of motion, specifically:
Where:
- is the final velocity (which is zero, since it stops completely after 197.4 m),
- is the initial velocity (70.4 m/s),
- is the acceleration (which we will find),
- is the distance (197.4 m in the first case and 44.2 m in the second).
Step 1: Calculate the acceleration
For the first part of the motion (stopping over 197.4 m), the final velocity m/s, and the initial velocity m/s. Using the equation:
Let’s calculate the value of :
So, the acceleration is .
Step 2: Calculate the speed after traveling 44.2 m
Now, using the same equation of motion to find the speed before it covers the final 44.2 m. We need to find the initial velocity for this part. The equation becomes:
Where:
- ,
- ,
- is what we need to find (the initial speed before the deceleration),
- (since it stops).
Rearranging the equation:
Thus, the speed of the jet before traveling the last 44.2 m is approximately 33.3 m/s.
Would you like further clarification or details on this solution? Here are some related questions for further practice:
- What is the total time taken for the jet to come to a stop from 70.4 m/s?
- What would the deceleration be if the jet stopped over a distance of 300 meters instead?
- How would the initial speed change if the stopping distance were doubled?
- How much time does the jet take to reduce its speed from 33.3 m/s to zero over the final 44.2 meters?
- Can you derive a formula for the distance covered during a deceleration from any speed to rest?
Tip: Always keep track of your signs when dealing with acceleration and deceleration, as confusion can lead to errors!
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Math Problem Analysis
Mathematical Concepts
Kinematics
Equations of Motion
Formulas
v^2 = u^2 + 2as
a = (v^2 - u^2) / (2s)
Theorems
Kinematic equations for uniformly accelerated motion
Suitable Grade Level
High School (Grades 10-12)
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