A particle is drop from a vertical height (h) and falls freely for a time(t) with the aid of a sketch explain how (h) varies with
(I) t
(ii) t square
To explain how the vertical height (h) of a particle varies with time (t) and with time squared (t^2), we can use a sketch or a graph.
I) Variation of height (h) with time (t):
- On the x-axis, represent time (t) and on the y-axis, represent height (h).
- Initially, when the particle is dropped, the height is at its maximum value, corresponding to the starting point.
- As time passes, the particle falls freely under gravity, and the height decreases.
- The downward slope of the graph represents the decreasing height as time progresses.
- Eventually, at time (t = 0), the particle reaches the ground, and the height becomes zero.
II) Variation of height (h) with time squared (t^2):
- On the x-axis, represent time squared (t^2) and on the y-axis, represent height (h).
- Initially, when the particle is dropped, the height is at its maximum value, corresponding to the starting point.
- As time passes, the height decreases, but at a non-linear rate.
- The graph of height (h) vs. time squared (t^2) will be a downward concave curve.
- The curve shows that the height decreases faster initially and then slows down as time increases.
- Eventually, at infinite time squared, the height becomes zero, representing the ground level.
It's important to note that the rate of decrease in height depends on the acceleration due to gravity, as well as any other external factors that may affect the motion of the particle.