Question

You release a cart from rest. It accelerates through two photogates. It crosses the first photogate with a speed of 0.404±0.0294 0.404 ± 0.0294 m/s. It crosses the second photogate 0.8118±0.0001 0.8118 ± 0.0001 seconds later with a speed of 0.68±0.0314 0.68 ± 0.0314 m/s.

Answer 1

Acceleration of cart,

a = vf - vi / tf - ti

a = (0.68 ± 0.0314 ) - (0.404 ± 0.0294) / (0.8118 ± 0.0001)

We know that,

when quantities are added or substraced, absolute errors are added.

a = (0.68 - 0.404) ± (0.0314 + 0.0294) /  (0.8118 ± 0.0001)

a = 0.276 ± 0.0608 /  (0.8118 ± 0.0001)

a = 0.276 ± (0.0608% / 0.276) / (0.8118 ± (0.0001% / 0.8118))

a = (0.276 / 0.8118) ± ((0.0608% / 0.276 + 0.0001% / 0.8118)

a = 0.339 ± 0.22041%

a =  0.339 ± (0.22041*0.339)

a = 0.339 ± 0.0749

acceleration a = 0.339 m/s^2

uncertainity = 0.0749 m/s^2