Question

Please help me?

Answer 1

Velocity `v(ms^-1)` satisfies `3.16<= v<= 3.78` and b) is the best answer.

Explanation:

Calculating the upper and lower bound helps you in this type of problem.

If the body travels the longest distance (`14.0 m`) in the shortest
time (`3.7 s`), the velocity is maximized. This is the upper bound
of the velocity `v_max`

`v_max` = `(14.0 (m))/(3.7 (s))` = `3.78(ms^-1)`.

Simirally, the lower bound of the velocity `v_min` is obtained as
`v_min` = `(13.6 (m))/(4.3 (s))` = `3.16(ms^-1)`.

Therefore, the velocity `v` stands between `3.16(ms^-1)` and `3.78(ms^-1)`. Choice b) fits this best.

Answer 2

Option (b)
`(3.45+-0.30)m/s`

Explanation:

if the Quantity is defined as `x=a/b`
let `Deltaa= "Absolute error for a"`
`Deltab= "Absolute error for b"`
`Deltax= "Absolute error for x"`
then The Maximum Possible Relative Error in x is
`(Deltax)/x=+-[(Deltaa)/a+(Deltab)/b]`

Now
Distance `=(13.8+-0.2)m`
`s=13.8 m` and `Delta s=0.2m`
Time `=(4.0+-0.3)m`
`t=4.0 m` and `Delta t=0.3m`

Velocity of Body Within error Limit is `v+Deltav`
Now `"velocity"="Distance"/"time"`
`v=s/t=13.8/4=3.45 m/s`

and Relative error in Velocity
`(Deltav)/v=+-[(Deltas)/s+(Deltat)/t]`
`(Deltav)/v=+-[(0.2)/13.8+(0.3)/4]=0.014+0.075=0.089`
Absolute Error in Velocity
`Deltav=0.089xxv=0.089xx3.45=0.307 m/s`

Hence

Velocity of Body Within error Limit is
`v+Deltav=(3.45+-0.30)m/s`

Option (b)

Hope You gets your answer.