The X-component of acceleration of the body is the rate of change of velocity of the body in the direction of X-axis.
Further Explanation:
Consider a body is moving with a uniform acceleration in [tex]x-y\text{ plane}[/tex].
Here, [tex]x[/tex] represents the X-axis and [tex]y[/tex] represents the Y-axis of the plane.
The rate of change of position of the body on x-y plane can be specified by the rate of change of position in the direction of x-axis and y-axis.
[tex]\vec r=\left( {x\hat i+y\hat j} \right){\text{ m}}[/tex]
Here, [tex]\vec r[/tex] is the position vector of the body, [tex]x[/tex] is the distance measure from origin in X-direction and [tex]y[/tex] is the distance measure from origin in Y-direction.
Similarly, the rate of change of velocity of the body can be specified by rate of change of velocity in direction of X-axis and Y-axis.
[tex]\dfrac{{d\vec v}}{{dt}}=\left( {\left( {\dfrac{{d{v_x}}}{{dt}}} \right)\hat i + \left( {\dfrac{{d{v_y}}}{{dt}}} \right)\hat j} \right){{{{\text{ m}}} \mathord{\left/ {\vphantom {{{\text{ m}}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}^2}[/tex] …… (1)
Here, [tex]\dfrac{{d\vec v}}{{dt}}[/tex] is the rate of change of velocity of body, [tex]\left( {\dfrac{{d{v_x}}}{{dt}}} \right)[/tex] is the rate of change of velocity in direction of X-axis and [tex]\left({\dfrac{{d{v_y}}}{{dt}}}\right)[/tex] is the rate of change of velocity in direction of Y-axis.
From the definition of acceleration,
The rate of change of velocity is acceleration and rate of change of velocity in X-direction is the acceleration in X-direction and rate of change of velocity in Y-direction is the acceleration in Y-direction.
So, equation (1) can be written as,
[tex]\boxed{a=\left( {{a_x}\hat i + {a_y}\hat j} \right){{{\text{ m}}} \mathord{\left/ {\vphantom {{{\text{ m}}} {{{\text{s}}^2}}}} \right. \kern-\nulldelimiterspace} {{{\text{s}}^2}}}}[/tex]
Here, [tex]a[/tex] represents the actual or resultant acceleration of the body, [tex]{a_x}[/tex] is the acceleration of the body in X-direction or rate of change of velocity in X-direction, [tex]{a_y}[/tex] is the acceleration of the body in Y-direction or rate of change of velocity in Y-direction.
Learn More:
1. Motion of a ball under the acceleration due to gravity https://brainly.com/question/10934170
2. A 30kg box being pulled on a carpeted floor https://brainly.com/question/7031524
3. A 50-kg meteorite moving at 1000 m/s strikes Earth https://brainly.com/question/6536722
Answer Detail:
Grade: Senior school
Chapter: Kinematics
Subject: Physics
Keywords:
x-component of acceleration, ax, component, acceleration, velocity, rate of change, time, X-axis, X-direction.
