Question

A body accelerates from rest with a uniform acceleration a for a time t.the uncertainty in a is 8%and the uncertainty in t is 4% .the uncertainty in the speed is

Answer 1

Given:

Uncertainty in acceleration(a) = 8%

Uncertainty in time(t) = 4%

To find:

The uncertainty in the speed

Calculation:

From the equations of motion, we know the relation

      $v=u+at$

Initial velocity will be zero as the body starts from rest.Therefore u=0

      $v=at$

Calculate the error in speed

      $\frac{\Delta v}{v} =\frac{\Delta a}{a} +\frac{\Delta t}{t}$

      $\frac{\Delta v}{v} =8+4$

      $\frac{\Delta v}{v} =12\%$

Final answer:

The uncertainty in the speed is 12%

Answer 2

V = U + at

therefore ∆v/v = ∆a/a + ∆ t/t

:. ∆v/v ×100 = ∆ a/a × 100 + ∆ t /t

:. error in v = 8%+4%

v = 12%

Final answer

The uncertainity of speed

= 12%