Answer:
11.7 s
Explanation:
In this problem, the rocket is moving in a uniform accelerated motion. We have the following data:
d = 223 m, the distance that the sled has to cover
[tex]a=3.25 m/s^2[/tex], the acceleration of the rocket
We can use therefore the following SUVAT equation:
[tex]d=ut+\frac{1}{2}at^2[/tex]
where
d is the distance
u = 0 is the initial velocity of the sled (it starts from rest)
t is the time
a is the acceleration
Re-arranging the equation and substituting the numbers, we find the time it takes for the rocket to cross the field:
[tex]d=\frac{1}{2}at^2\\t=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2(223)}{3.25}}=11.7 s[/tex]
The equation of motion is the relation between the distance, velocity, acceleration and time of a moving body.
The time will it take the sled to cross the field starting from rest is 11.7 seconds.
The equation of motion is the relation between the distance, velocity, acceleration and time of a moving body.
The second equation of the motion for distance can be given as,
[tex]s=ut+\dfrac{1}{2}a t^2[/tex]
Here, [tex]u[/tex] is the initial body, [tex]a[/tex] is the acceleration of the body and [tex]t[/tex] is the time taken by it.
Given information-
The field is 223 m across.
Sled need to be accelerates at a rate of 3.25 m/s squared.
As the initial speed is zero thus put the values in the above formula to find the required time as,
[tex]223=0+\dfrac{1}{2}\times3.25\times t^2\\t=11.7\rm s[/tex]
Hence the time will it take the sled to cross the field starting from rest is 11.7 seconds.
Learn more about the equation of motion here;
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