Velocity is always tangent to the path of motion To see if y

Velocity is always tangent to the path of motion. To see if you really understand this concept determine the angle of the velocity vector from 2 horizontal when the particle is at an x-coordinate of 2 meters. The a particle follows the path defined by y = x^2 - x + 3 (where x and y are in meters). 11.3 degrees 18.4 degrees 21.8 degrees 45 degrees 68.2 degrees 71.6 degrees 78.7 degrees

Solution

Given

Displacement y = x² -x + 3

Since velocity is always tangential to the path of motion, the tangent of angle it makes with the horizontal is nothing but the slope of the path at that particular point.

slope, m dy / dx = 2x - 1

Slope at x = 2

m = 2(2) - 1

= 3

By definition slope, m = tan (theta)

where theta is the angle made by velocity vector with the horizontal.

3 = tan(theta)

theta = tan^-1 (3)

theta = 71.6 degrees

Thus the velocity vector makes an angle of 71.6 degrees with the horizontal at x = 2 m.