When Does Runner B Pass Runner A?

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In summary, Runner A travels a distance of 60m in 10 seconds at a constant speed of 6.0m/s. Runner B travels a distance of 70m in 10 seconds with a steady acceleration from 4.0m/s to 10.0m/s. Runner B surpasses Runner A by 10m at 10 seconds, but the time at which Runner B passed Runner A cannot be determined without additional information.
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xcompulsion
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Homework Statement


Runner A runs at 6.0m/s for 10s. Runner B accelerates from 4.0 m/s to 10.0 m/s steadily in 10s. How far does Runner A go in 10s? How far does Runner B go in 10s? At what time did Runner B pass Runner A if they were both at the same position at t=0?

Homework Equations


d= v*t, d = 1/2(v1+v2)*t

The Attempt at a Solution



Runner A:
d = v*t
d = (6.0m/s)(10s)
d = 60m

Runner B:
d = 1/2(v1+v2)*t
d = 1/2(4m/s+10m/s)*(10s)
d = 1/2(14m/s)*(10s)
d= 70m

so therefore at 10s, Runner B has already surpassed Runner A by 10m. But how would you find when Runner B passed Runner A?


Many thanks.
 
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  • #2
Do you see that you want to find t such that vt = ½(v1+v2)t? How can you write v2 in terms of t?
 
  • #3
Tedjn said:
Do you see that you want to find t such that vt = ½(v1+v2)t? How can you write v2 in terms of t?

im sorry. i don't understand..
 

FAQ: When Does Runner B Pass Runner A?

How do you calculate the point of intersection between two lines?

To calculate the point of intersection between two lines, you can use the simultaneous equations method or the substitution method. These methods involve solving the equations of the two lines for the variables, and then plugging those values into the equations to find the coordinates of the intersection point.

What is the formula for calculating the distance between two points?

The formula for calculating the distance between two points is the Pythagorean theorem, which states that the square of the distance between two points (d) is equal to the sum of the squares of the differences between their coordinates (x2-x1) and (y2-y1).

How do you determine if two points will ever meet?

If two points are moving along the same line, they will eventually meet at the point where their coordinates are equal. However, if the points are moving along different lines, you can determine if they will ever meet by setting up and solving equations to find if their coordinates will ever be equal at the same time.

What is the significance of finding the point where two lines intersect?

The point of intersection between two lines is significant because it represents a solution to a problem or system of equations. It can also be used to find the slope and y-intercept of the lines, and can provide insight into the relationship between the lines.

Can you use calculus to calculate when two points will meet?

Yes, you can use calculus to calculate when two points will meet. This method involves finding the derivative of the equations of the two lines and setting them equal to each other to find the x-coordinate of the point of intersection. Then, you can plug this x-coordinate into either equation to find the y-coordinate of the point of intersection.

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