The average speed in m/s of a person that jogs eight complete laps around a 400m track in a total time of 15.1 min is 0.44m/s.
<h3>How to calculate average speed?</h3>
Average speed of a moving body can be calculated by dividing the distance moved by the time taken.
Average speed = Distance ÷ time
According to this question, a person jogs eight complete laps around a 400m track in a total time of 15.1 min. The average speed is calculated as follows:
15.1 minutes in seconds is as follows = 906 seconds
Average speed = 400m ÷ 906s
Average speed = 0.44m/s
Therefore, the average speed in m/s of a person that jogs eight complete laps around a 400m track in a total time of 15.1 min is 0.44m/s.
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Wood i think could be wrong
Acceleration in a velocity vs time graph is just the slope at that point. The reason for that is because the definition of acceleration is the change in velocity per unit of time. In this case we want instantaneous, which is the derivative or tangent line at that point.
At 3s we can see the slope is 0, so that means his acceleration is zero. That means he was moving at a constant velocity
At 5s we can see that the slope is negative. And from 5s to 6s the change in velocity is -5m/s^2
At 7s we can see the slope is very positive. And from 7s to 8s the change in velocity is +15m/s^2
And again, at 9s the slope is 0 so his acceleration is also zero. He’s moving at a constant velocity
If you take the integral of a velocity vs time graph, you get position. So the area underneath a velocity vs time graph is the distance traveled. Anything below the x axis is considered negative distance. We need to take the area of a triangle and the area of two rectangles to find the distance.
So, let’s do the two rectangles first. From 8s to 9s it is a width of 1 and a length of 40. So the area would be 40 meters. Let’s do the second rectangle. From 7s to 8s it is a width of 1. Then the length goes up to 25. So the area is 25 meters.
Now the triangle, the base is 1 and the height is 15. Divide 15 in half to get 7.5 meters
25 + 40 + 7.5 = 72.5 meters
For rectilinear motions, derived formulas all based on Newton's laws of motion are formulated. The equation for acceleration is
a = (v2-v1)/t, where v2 and v1 is the final and initial velocity of the rocket. We know that at the end of 1.41 s, the rocket comes to a stop. So, v2=0. Then, we can determine v1.
-52.7 = (0-v1)/1.41
v1 = 74.31 m/s
We can use v1 for the formula of the maximum height attained by an object thrown upwards:
Hmax = v1^2/2g = (74.31^2)/(2*9.81) = 281.42 m
The maximum height attained by the model rocket is 281.42 m.
For the amount of time for the whole flight of the model rocket, there are 3 sections to this: time at constant acceleration, time when it lost fuel and reached its maximum height and the time for the free fall.
Time at constant acceleration is given to be 1.41 s. Time when it lost fuel covers the difference of the maximum height and the distance travelled at constant acceleration.
2ax=v2^2-v1^2
2(-52.7)(x) = 0^2-74.31^2
x =52.4 m (distance it covered at constant acceleration)
Then. when it travels upwards only by a force of gravity,
d = v1(t) + 1/2*a*t^2
281.42-52.386 = (0)^2+1/2*(9.81)(t^2)
t = 6.83 s (time when it lost fuel and reached its maximum height)
Lastly, for free falling objects, the equation is
t = √2y/g = √2(281.42)/9.81 = 7.57 s
Therefore, the total time= 1.41+6.83+7.57 = 15.81 s
