a particle moving in a straight line with constant acceleration passing over distances x,y,z in equal consecutive interval of time(t).find the relation between x,y and z..and the acceleration of the body.
To find the relation between x, y, and z, we can use the equations of motion. Let's assume that the particle starts from rest at time t = 0.
Since the particle is moving in a straight line with constant acceleration, we can use the equation of motion:
x = (1/2) * a * t^2 -- Equation 1
y = a * t^2 -- Equation 2
z = (3/2) * a * t^2 -- Equation 3
Here, x, y, and z represent the distances covered by the particle in equal consecutive time intervals, and a represents the acceleration of the body.
To find the relation between x, y, and z, we can solve these equations.
First, let's solve Equation 2 for t:
t^2 = y / a
Next, substitute the value of t^2 in Equations 1 and 3:
x = (1/2) * a * (y / a) --> x = (1/2) * y -- Equation 4
z = (3/2) * a * (y / a) --> z = (3/2) * y -- Equation 5
So, we have found the relation between x, y, and z:
x = (1/2) * y
z = (3/2) * y
The acceleration of the body (a) does not affect the relation between x, y, and z. It only affects the magnitudes of these distances.
Therefore, the relation between x, y, and z is x = (1/2) * y and z = (3/2) * y. The acceleration of the body is not needed to determine this relation.