I am currently working with some velocity and acceleration vectors and I am a bit unsure about how to interpret the results. Consider the fact that I have 3 points 1.(x1,y1) @ t = 0.0s, 2.(x2,y2) @ t = 0.1s, and 3.(x3,y3) @ t = 0.2s.
Using these coordinates I calculate a velocity vector between points 1 and 2 and another velocity vector between points 2 and 3. I then calculate an acceleration vector using the 2 velocity vectors over 0.2s.
If I were to calculate a dot product between the acceleration vector and the first velocity vector and use that along with the magnitude of the first vector and magnitude of the acceleration vector to calculate the angle between the acceleration vector and the velocity vector, what does that angle represent and how can I interpret it?
I have the following code to calculate these vectors if that helps. I am just trying to gain a better intuition of what the dot product between the first velocity vector and the acceleration vector actually means
first_point = all_coordinates[i][j] second_point = all_coordinates[i][j+1] third_point = all_coordinates[i][j+2] first_vector = (second_point-first_point,second_point-first_point) second_vector = (third_point-second_point,third_point-second_point) first_vector_magnitude = math.sqrt((first_vector)**2 + (first_vector)**2) second_vector_magnitude = math.sqrt((second_vector)**2 + (second_vector)**2) time_interval = 0.1 velocity_vector1 = (first_vector/time_interval,first_vector/time_interval) velocity_vector2 = (second_vector/time_interval,second_vector/time_interval) acceleration_vector = (((velocity_vector2-velocity_vector1)/0.2),((velocity_vector2-velocity_vector1)/0.2)) acceleration_vector_magnitude = math.sqrt((acceleration_vector)**2 + (acceleration_vector)**2) dot_product = ((first_vector*acceleration_vector)+(first_vector*acceleration_vector)) angle = np.arccos(round((dot_product/(first_vector_magnitude*acceleration_vector_magnitude)),2))