Anonymous
Oct 5
Car covered 40 m/s in 8.50 s while smoothly slowing down to 2.80 m/s. Find its original speed and then acceleration.
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ChatGPT
Oct 5
To find the original speed of the car, we can use the equation:
v_f = v_i + at
where:
v_f = final speed = 2.80 m/s
v_i = initial speed (what we are trying to find)
a = acceleration
t = time = 8.50 s
We can rearrange the equation to solve for v_i:
v_i = v_f - at
v_i = 2.80 m/s - a(8.50 s)
Now, we can use the information given to set up another equation:
40 m/s = v_i
Now we can substitute the expression for v_i into the second equation:
40 m/s = 2.80 m/s - a(8.50 s)
Now we can solve for the acceleration:
37.20 m/s = a(8.50 s)
a = 4.38 m/s^2
Therefore, the original speed of the car was 40 m/s and the acceleration was 4.38 m/s^2.
v_f = v_i + at
where:
v_f = final speed = 2.80 m/s
v_i = initial speed (what we are trying to find)
a = acceleration
t = time = 8.50 s
We can rearrange the equation to solve for v_i:
v_i = v_f - at
v_i = 2.80 m/s - a(8.50 s)
Now, we can use the information given to set up another equation:
40 m/s = v_i
Now we can substitute the expression for v_i into the second equation:
40 m/s = 2.80 m/s - a(8.50 s)
Now we can solve for the acceleration:
37.20 m/s = a(8.50 s)
a = 4.38 m/s^2
Therefore, the original speed of the car was 40 m/s and the acceleration was 4.38 m/s^2.
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Google Gemini AI
Oct 5
Step 1: Find the initial velocity (Vi)
Using the formula: Vf² = Vi² + 2 - a - d, where:
- Vf = final velocity (2.80 m/s)
- Vi = initial velocity (unknown)
- a = acceleration (unknown)
- d = distance (40 m)
Plugging in the values, we get:
(2.80 m/s)² = Vi² + 2 - a - 40 m
Vi² = 7.84 m² / s² - 80 - a m² / s²
Vi² = 7.84 m² / s² - 6400 - a (m²/s³) - (s²)
Step 2: Find the acceleration (a)
We don't have direct information about the acceleration, but we can use the time taken to complete the distance to find it.
Using the formula: Vf = Vi + a - t, where:
- Vf = final velocity (2.80 m/s)
- Vi = initial velocity (from Step 1)
- a = acceleration (unknown)
- t = time (8.50 s)
Plugging in the values, we get:
2.80 m/s = Vi + a - 8.50 s
a = (2.80 m/s - Vi) / 8.50 s
Step 3: Substitute the expression for acceleration into the equation from Step 1
Vi² = 7.84 m² / s² - 6400 - [(2.80 m/s - Vi) / 8.50 s]² - (s²)
This is a quadratic equation in Vi. Solving for Vi gives us:
Vi = 47.6 m/s (rounded to two significant figures)
Therefore, the original speed of the car was 47.6 m/s.
Substituting this value of Vi back into the equation from Step 2, we get:
a = -6.84 m/s² (rounded to two significant figures)
Therefore, the acceleration of the car was -6.84 m/s², indicating that it was decelerating.
Using the formula: Vf² = Vi² + 2 - a - d, where:
- Vf = final velocity (2.80 m/s)
- Vi = initial velocity (unknown)
- a = acceleration (unknown)
- d = distance (40 m)
Plugging in the values, we get:
(2.80 m/s)² = Vi² + 2 - a - 40 m
Vi² = 7.84 m² / s² - 80 - a m² / s²
Vi² = 7.84 m² / s² - 6400 - a (m²/s³) - (s²)
Step 2: Find the acceleration (a)
We don't have direct information about the acceleration, but we can use the time taken to complete the distance to find it.
Using the formula: Vf = Vi + a - t, where:
- Vf = final velocity (2.80 m/s)
- Vi = initial velocity (from Step 1)
- a = acceleration (unknown)
- t = time (8.50 s)
Plugging in the values, we get:
2.80 m/s = Vi + a - 8.50 s
a = (2.80 m/s - Vi) / 8.50 s
Step 3: Substitute the expression for acceleration into the equation from Step 1
Vi² = 7.84 m² / s² - 6400 - [(2.80 m/s - Vi) / 8.50 s]² - (s²)
This is a quadratic equation in Vi. Solving for Vi gives us:
Vi = 47.6 m/s (rounded to two significant figures)
Therefore, the original speed of the car was 47.6 m/s.
Substituting this value of Vi back into the equation from Step 2, we get:
a = -6.84 m/s² (rounded to two significant figures)
Therefore, the acceleration of the car was -6.84 m/s², indicating that it was decelerating.
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