Question

can i use distance covered/time formula in non uniform acceleration​

Answer 1

Answer:

The same way as you do for a uniform acceleration … you draw the acceleration-time graph… the area under that gives you the velocity-time graph and the area under that gives you the displacement-time graph.

Distance comes from careful examining the displacement-time graph.

Arithmetically, you have to solve:

[math]\ddot s = f(t)[/math]

(The dots indicate differentiation with respect to time.)

The trouble is that f can be any function at all… so the solutions are arbitrarily complicated. There is no single method to use, and no set of equation like you have for uniform acceleration.

It can get easier if the rate of change of acceleration is some easy function, like um, what’s the easiest function… I know: a constant…

[math]\dot a = j[/math]

…where j is an arbitrary constant, then

[math]a(t) = a_0 + jt[/math]

[math]v(t) = v_0 + a_0t + \frac{1}{2}jt^2[/math]

[math]s(t) = s_0 + v_0t + \frac{1}{2}a_0t^2 + \frac{1}{6}jt^3[/math]

See how that works? It’s successive integration… which is a fancy algebra way of saying you find the area under the graph.

Note: [math]x_0 = x(t=0) \; : x \in \{a,v,s\}[/math]

Explanation:

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