Question

A train travels 64.7±0.5 metres in 8.65±0.05 seconds. What is the absolute uncertainty in its speed?

Answer 1

The Speed of the train is 7.48 +0.1 ms⁻¹

GIVEN

Distance travelled by train = 64.7 + 0.5 meters

Time taken = 8.65 +0.05 seconds.

TO FIND

Absolute uncertainty in speed

SOLUTION

We can simply solve the above problem as follows -

We know that,

Speed = distance / time

Speed = 64.7/8.65 = 7.48 ms⁻¹

We know that ,

If

$y = \frac{a}{b}$

Then,

$\frac{Δy}{y} = \frac{Δa}{a} + \frac{Δb}{b}$

Therefore,

$\frac{Δy}{7.48} = \frac{0.5}{64.7} + \frac{0.05}{8.65}$

Δy = 0.12 × 7.48

Δy = 0.089 ~ 0.1 ms⁻¹

Hence, The Speed of the train = 7.48 +0.1 ms⁻¹

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