Physics MOTION IN STRAIGHT LINE

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MOTION IN STRAIGHT LINE

Instantaneous Acceleration

Suppose a particle moving in a straight line has velocity `v` at time `t` at position `A` and velocity `v + Delta v` at time `t + Delta t` at position `B` . the average acceleration over time interval `Delta t` can be written as `a = (Delta v)/(Delta t)`

To get instantaneous acceleration at time `t` .

`a = lim_(Deltat->0) ((Delta v)/(Deltat)) = (dv)/(dt)`

`a= (dv)/(dt) = d/(dt) ((dx)/(dt)) = (d^2x)/(dt^2)`

`a= (dv)/(dt) = (dv)/(dx) quad(dx)/(dt) = v ((dv)/(dx))`

`a= (dv)/(dt) = (d^2x)/(dt^2) =v((dv)/(dx))`

Average Acceleration

Average acceleration is the rate at which velocity changes. Average acceleration is the change in velocity divided by an elapsed time. For instance, if the velocity of a particle increases from `v_1` to `v_2` in `t` seconds, its average acceleration would be

`text(Average Acceleration)=(v_2-v_1)/t`

or `text(Average acceleration)=(Deltatext(Velocity))/(Deltatext(Time))`