Need quick help with finding positional equation

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In summary, a tractor with a speed of 40.0km/h and a Tesla with a speed of 80.0km/h are approaching each other on a winding mountain road. Both vehicles have a constant acceleration of 5.00m/s^2 in opposite directions. The initial distance between them is 60.0m. Using positional equations and considering one vehicle as the frame of reference, it can be determined whether they will collide and at what speed and location, or if they will stop before reaching each other.
  • #1

Homework Statement

A huge tractor and a Tesla full of school children come driving along a winding
mountain road, in opposite directions. The tractor has a speed of
40.0km/h and the car zooms along with 80.0km/h. The Tesla suddenly comes around a
corner, sees the tractor, and they both immediately start braking, both with
constant accelerations of 5.00m/s^2 (opposite to their directions of motion).
a) If the initial distance between the two is 60.0m, do they hit each other? If
so, where, and with what relative speed on impact? If not, what is the distance
between the two when they both stop?

Homework Equations

x(t)= -a/2*t2 + v*t + x

Dont know how to find the positional equations of the two vehicles and then solve for t to find where they crash.
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  • #2
Pick one of the vehicles as your frame of reference (so its position is always at x=0) and use the combined relative velocities, accelerations, etc. in your equation to calculate the other vehicle's position. See how far that gets you.
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1. What is a positional equation?

A positional equation is a mathematical equation that represents the relationship between an object's position and time. It is commonly used in physics and engineering to describe the motion of objects.

2. How do I find the positional equation?

To find the positional equation, you will need to know the initial position and velocity of the object, as well as the acceleration. Then, you can use the formula x = x0 + v0t + 1/2at2, where x is the position at time t, x0 is the initial position, v0 is the initial velocity, and a is the acceleration.

3. Can a positional equation be used for any type of motion?

Yes, a positional equation can be used to describe the motion of objects in one, two, or three dimensions, as long as the acceleration is constant. It can also be used for both linear and rotational motion.

4. How accurate is a positional equation?

A positional equation is accurate as long as the acceleration remains constant. However, if there are external forces acting on the object that cause changes in acceleration, the equation may not accurately predict the object's position.

5. What is the difference between a positional equation and a velocity equation?

A positional equation describes the position of an object at a specific time, while a velocity equation describes the object's velocity at a specific time. They are related, as the derivative of the positional equation is the velocity equation and the second derivative is the acceleration equation.

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