Respuesta :
The flea's acceleration is 1,000 m/s².
Further explanation
The problem we overlook this time is about uniformly accelerated motion.
The list of variables to be considered is as follows.
[tex]\boxed{u \ or \ v_i = initial \ velocity}[/tex]
[tex]\boxed{u \ or \ v_t \ or \ v_i = terminal \ or \ final \ velocity}[/tex]
[tex]\boxed{a = acceleration \ (constant)}[/tex]
[tex]\boxed{d = distance \ travelled}[/tex]
Given that a take-off speed of 1.0 m/s over a distance of 0.50 mm.
The initial speed was zero from rest. It was asked about flea's acceleration when she extends her legs.
The formula we follow for this problem are as follows:
[tex]\boxed{ \ v^2 = u^2 + 2ad \ }[/tex]
- a = acceleration (in m/s²)
- u = initial velocity = 0 m/s
- v = take off speed = 1.0 m/s
- d = distance travelled = 0.50 mm
Converted 0.50 mm to meters: [tex]\boxed{0.50 \ mm = 0.50 \times 10^{-3} \ m = 5.0 \times 10^{-4} \ m}[/tex]
Steps:
We set the formula so that the acceleration becomes the subject.
[tex]\boxed{ \ v^2 = u^2 + 2ad \ }[/tex]
[tex]\boxed{ \ v^2 - u^2 = 2ad \ }[/tex]
[tex]\boxed{ \ 2ad = v^2 - u^2 \ }[/tex]
[tex]\boxed{ \ a = \frac{v^2 - u^2}{2d} \ }[/tex]
Substitute all data into equations.
[tex]\boxed{ \ a = \frac{(1.0)^2 - (0)^2}{2(5.0 \times 10^{-4})} \ }[/tex]
[tex]\boxed{ \ a = \frac{1}{10 \times 10^{-4}} \ }[/tex]
[tex]\boxed{ \ a = \frac{1}{1 \times 10^{-3}} \ }[/tex]
[tex]\boxed{ \ a = 1 \times 10^{3}\ = 1,000 \ m/s^2 \ }[/tex]
We get the flea's acceleration, i.e., 1,000 m/s².
Learn more
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Keywords: flea, when jumping, rapidly extends its legs, take-off speed, initial velocity, distance, acceleration, uniformly accelerated motion, convert
The Flea acceleration as it extends its leg is [tex]\fbox{\begin\\\ 1000\ m/s^{2}\\\end{minispace}}[/tex].
Further explanation:
Given:
The takeoff speed of the flea is [tex]1.0\ \text{m/s}[/tex].
The distance cover by flea is [tex]0.50\ \text{m/s}[/tex].
To find:
The acceleration of the flea as it extended it legs.
Formula used:
The acceleration of the flea can be obtained by the given formula.
[tex]\fbox{\begin\\\ \math v^{2}=u^{2}+2as\\\end{minisapce}}[/tex] ....(1)
Here, [tex]v[/tex] is the final velocity of flea, [tex]u[/tex] is the initial velocity of flea, [tex]a[/tex] is the acceleration of the flea, [tex]s[/tex] is the distance cover by the flea.
Calculation:
The initial velocity of flea is [tex]0[/tex].
The final velocity of flea is [tex]1.0\text{m/s}[/tex].
The distance cover by flea is in millimeter.
Convert millimeter into meter as follows.
[tex]\fbox{\begin\\\ \begin{aligned}0.50 \text{ mm}&=\dfrac{0.50}{1000}\text{ m}\\&=0.0005\text{ m}\end{aligned}\\\end{minispace}}[/tex]
Now substitute [tex]0[/tex] for [tex]u[/tex], [tex]1.0[/tex] for [tex]v[/tex] and [tex]0.0005[/tex] for [tex]s[/tex] in equation (1) to obtain the value of acceleration.
[tex]\begin{aligned}1^{2}&=0^{2}+(2a\times(0.0005))\\1&=0.001a\\a&=\dfrac{1}{0.001}\\a&=1000\end{aligned}[/tex]
Therefore, the acceleration of the flea is as it extends its leg is [tex]\fbox{\begin\\\ 1000\ m/s^{2}\\\end{minispace}}[/tex].
Learn more:
1. Solution of linear equation: //brainly.com/question/1682776
2. Magnitude of the acceleration https://brainly.com/question/1597065
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Speed and distance
Keywords: Flea, jump, legs, takeoff speed, acceleration , distance cover, 0.05 mm, 1000 meter per second square. Initial velocity, Final velocity
