Calculating velocity from speed and direction - c++

Question

I have an object which wants to move from point A to point B, at a certain speed (using SFML C++).
sf::Vector2f aPos; //sf::Vector2f has two members x and y, stored as floats
sf::Vector2f bPos;
float speed; //pixels per tick
I want to use these variables to find out a velocity, with an x speed and a y speed, such that the hypotenuse of vel.x and vel.y has length speed, and has the same bearing as that from point aPos to point bPos.
sf::Vector2f vel;
What is the simplest and most effective function that I can write, which takes sf::Vector2f aPos, sf::Vector2f bPos and float speed as arguments, and returns sf::Vector2f vel
sf::Vector2f findVel(sf::Vector2f aPos, sf::Vector2f bPos, float speed) {
sf::Vector2f vel;
//the code I need
return vel;
}
Thank you in advance! :)

Answer 1

Taking k_g's answer, we can actually shorten it quite a bit given that Vector2f has operator overloads. It can simply become:
sf::Vector2f findVel(const sf::Vector2f& aPos, const sf::Vector2f& bPos, float speed) {
sf::Vector2f disp = bPos-aPos;
float distance = sqrt(disp.x*disp.x+disp.y*disp.y); // std::hypot(disp.x, disp.y) if C++ 11
return disp * (speed/distance);
}
This also allows us to benefit from any optimizations that might have been built into the Vector class for operations.
Note the change to const & for the input parameters; no need to make a copy of them since you aren't manipulating them.

Answer 2

well, we know that speed == distance/time and velocity == displacement/time.
Solving for 1/time in the first equation, we get 1/time==speed/distance. We substitute this into the second equation to get velocity == displacement*speed/distance.
Using this formula, we get the following function
sf::Vector2f findVel(sf::Vector2f aPos, sf::Vector2f bPos, float speed) {
sf::Vector2f vel;
float dispx = bPos.x-aPos.x;
float dispy = bPos.y-aPos.y;
float distance = sqrt(dispx*dispx+dispy*dispy);
vel.x = dispx*speed/distance;
vel.y = dispy*speed/distance;
return vel;
}