Displacement and Time Relationship in Physics
How does displacement vary with time when acceleration is constant and the initial velocity is zero?
When acceleration is constant and the initial velocity is zero, how does displacement vary with time?
Is displacement directly proportional to time in this scenario?
Displacement and Time Relationship
When acceleration is constant and the initial velocity is zero, displacement varies with time as a parabolic function, increasing at an increasing rate.
The rate of displacement increase depends on the magnitude of acceleration. The greater the acceleration, the greater the rate of increase of displacement.
When acceleration is constant and the initial velocity is zero, the relationship between displacement and time follows a parabolic function. This means that as time progresses, the displacement increases at an increasing rate. In other words, the object covers more distance in less time with constant acceleration and zero initial velocity.
The mathematical representation of this relationship is given by the equation d = 1/2at^2, where d represents displacement, a is the acceleration, and t is the time elapsed. The equation can be derived from the fundamental equation of motion v^2 = 2as, where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration, and s is the displacement.
By integrating the equation v = at with respect to time, we get s = 1/2at^2, which shows the relationship between displacement and time in the scenario of constant acceleration and zero initial velocity.
Therefore, in this scenario, displacement is not directly proportional to time, but it follows a parabolic function. The rate of change of displacement with time is determined by the acceleration, with greater acceleration leading to a faster increase in displacement over time.