Respuesta :
Answer:
The distance traveled by Tina before passing David is 900 m
Given:
Initial speed of David, [tex]u_{D} = 30 m/s[/tex]
Acceleration of Tina, [tex]a_{T} = 2.0 m/s^{2}[/tex]
Solution:
Now, as per the question, we use 2nd eqn of motion for the position of David after time t:
[tex]s = u_{D}t + \frac{1}{2}at^{2}[/tex]
where
s = distance covered by David after time 't'
a = acceleration of David = 0
Thus
[tex]s = 30t[/tex]
Now, Tina's position, s' after time 't':
[tex]s' = u_{T}t + \frac{1}{2}a_{T}t^{2}[/tex]
where
[tex]u_{T} = 0[/tex], initially at rest
[tex]s' = 0.t + \frac{1}{2}\times 2t^{2}[/tex]
[tex]s' = t^{2}[/tex] (1)
At the instant, when Tina passes David, their distances are same, thus:
s = s'
[tex]30t = t^{2}[/tex]
[tex]t(t - 30) = 0[/tex]
t = 30 s
Now,
The distance covered by Tina before she passes David can be calculated by substituting the value t = 30 s in eqn (1):
[tex]s' = 30^{2}[/tex] = 900 m
The distance covered by Tina before passing David at an acceleration rate of 2 m/s² is 900 meters.
Given to us
Velocity of David, v = 30 m/s
Acceleration of Tina, a = 2 m/s²
Let the time taken by Tina pass David is t.
What is the Distance traveled by David before Tina pass him?
According to the given information, the distance traveled by Tina will be the same as the distance traveled by David between Tina when she was at rest and when Tina passes her.
Distance traveled by Tina = Distance traveled by David
Distance traveled by David,
[tex]s = v \times t\\\\ = 30 \times t =30t[/tex]
What is the time taken by Tina to pass David?
Using the second equation of Motion
[tex]s= ut +\dfrac{1}{2}at^2[/tex]
Substitute,
[tex]30t= (0)t +\dfrac{1}{2}(2)t^2[/tex]
[tex]t = 30\rm\ sec[/tex]
Thus, the time taken by Tina to pass David is 30 seconds.
How far does Tina drive before passing David?
We have already discussed,
Distance traveled by Tina = Distance traveled by David,
therefore,
[tex]s = v \times t\\\\ = 30 \times 30 =900\rm\ meters[/tex]
Hence, the distance covered by Tina before passing David at an acceleration rate of 2 m/s² is 900 meters.
Learn more about the Equation of motion:
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