Question

Question #32e56

Answer 1

A particle having initial velocity u , moving with uniform acceleration a covers a distance `S_t` in t th sec.

Let us recall the deduction of the relation among these quantities considering the average velocity of the particle for time `tin[(t-1),t]`

Velocity of the particle after (t-1) sec`=v_("t-1")=u+a(t-1)`

Velocity of the particle after t sec`=v_t=u+at`

Average velocity for `tin[(t-1),t]` is `v_"avg"=(v_("t-1")+v_t)/2`

`=>v_"avg"=(2u+a(2t-1))/2`
`=>v_"avg"=u+1/2a(2t-1)`

So `S_t=v_"avg"xx t^" th" sec=v_"avg"xx1sec`#

`S_t =u+1/2a(2t-1)`

Apparently the equation appears false according to dimension method. Since its LHS has dimension `[L]` and RHS has dimension `[LT^-1]` .
Here `S_t` represents distance traversed by the particle in t th sec which is actually a time interval of 1 sec. This 1 sec is multiplied in RHS and not visible as variable(t). The dimension of RHS is `[LT^-1]`without this invisible t.

If it is multiplied by dimension of time `[T]` for 1 sec, then the satisfaction of dimension will be found.