The equation for the coordinate of a material point moving along the Ox axis has the form x = 10 + 4t + 2t ^ 2 (values are expressed in SI). determine the nature of the point movement. find the starting coordinate, starting speed and acceleration of the point.
x = 10 + 4 * t + 2 * t ^ 2 – the equation of motion of a material point.
It is required to determine the nature of motion of a material point, the initial coordinate X0, the initial velocity V0 and the acceleration a.
The general equation of motion is:
x = X0 + V0 * t + t ^ 2/2.
Let’s equate both equations:
10 + 4 * t + 2 * t ^ 2 = X0 + V0 * t + a * t ^ 2/2.
By substituting the values, we determine:
X0 = 10, V0 = 4 m / s, a = 4 m / s ^ 2.
According to the data obtained, it can be seen that the movement starts from the coordinate X0 = 10, the movement is uniformly accelerated and directed towards the positive side of the ОX axis.
Answer: the motion is uniformly accelerated, directed towards the positive side of the ОХ axis, X0 = 10, V0 = 4 m / s, a = 4 m / s ^ 2.