- #1
Pushoam
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Homework Statement
Homework Equations
The Attempt at a Solution
The two particles are supposed to move along the same line.
And the two radius vector could be anything.
Is this correct?
Two cars do not need to be moving along the same line in order to collide.Pushoam said:The two particles are supposed to move along the same line.
YesTSny said:Can you write down a vector equation using r1, v1, and t that would represent the position of particle 1 at time t?
Good.Pushoam said:Yes
r1 (t) = r1 + v1 t
r2 (t) = r2 + v2 t ,for uniform motion
Now , collision of the two particles at time t means r1 (t) = r2 (t)
⇒ r1 - r2 = t (v2 - v1)
Not much left to do except interpret what you have.What to do next?
TSny said:Not much left to do except interpret what you have.
Yes, even if the trajectory of the two cars make V shape, they will collide.TSny said:Two cars do not need to be moving along the same line in order to collide.
That can't be exactly right, since relative velocity cannot equal displacement (they have different units).Pushoam said:The collision will occur only if at some time t, the relative velocity becomes equal and opposite to the initial relative displacement between the two particles.
No, you can't just drop the time. However, the time of the collision could be any time. So, can you express what this equation says about the relation between the four vectors r1, r2, v1, and v2 in order for a collision to eventually occur?Should I remove t in r1 - r2 = t (v2 - v1) ?
"Dropping" time would be like setting t=1 but there is no reason to only consider collisions occurring at t=1...Look at this equation:Pushoam said:Why can't I drop the time?
This is an equation of vectors, with time being a scalar. Are you able to solve this equation for the scalar t, and then put that back into the equation for t? That will give a relationship between the 4 vectors which does not involve time, which is as good as you can get. (That relation also has a simple intuitive interpretation which could've skipped past any considerations of time.)Pushoam said:r1 - r2 = t (v2 - v1) ?
It depends what you mean by that. You do not care when they collide, only whether they collide.Pushoam said:the time of collision can't be anytime.
Yes, I am.Hiero said:Are you able to solve this equation for the scalar t, and then put that back into the equation for t?
Is following the intuitive interpretation?Hiero said:(That relation also has a simple intuitive interpretation which could've skipped past any considerations of time.)
Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.
Vectors are mathematical quantities that have both magnitude (size) and direction.
To calculate the velocity of two particles that are going to collide, you need to use the principles of vector addition. You can add the individual velocities of the particles to find the total velocity at the point of collision.
Velocity is a vector quantity that includes both magnitude and direction, while speed is a scalar quantity that only includes magnitude. Velocity takes into account the direction of motion, while speed does not.
No, kinematics equations can only predict the motion of objects based on their initial conditions. They cannot predict the exact moment of collision between two particles as it depends on external factors such as forces and interactions between the particles.