Question

initial velocity of a particle moving along straight line with constant acceleration is (20+-2)m/s,if it's acceleration is a=(5+-0.1)m/s,then velocity of a particle with error, after time t =(10+-1)s,is​

Answer 1

Given

u = Initial velocity = $(20\pm2)\ \text{m/s}$

a = Acceleration = $(5\pm 0.1)\ \text{m/s}$

t = Time taken = $(10\pm 1)\ \text{m/s}$

To find

Final velocity of the particle

Solution

v = Final velocity

$v=u+at\\\Rightarrow v=20+5\times 10\\\Rightarrow v=70\ \text{m/s}$

The error's are

$du$ = $\pm 2$

$da$ = $\pm 0.1$

$dt$ = $\pm 1$

Differentiate the above equation with respect to time

$\dfrac{dv}{dx}=\dfrac{du}{dx}+\dfrac{dat}{dx}\\\Rightarrow \dfrac{dv}{dx}=\dfrac{du}{dx}+t\dfrac{da}{dx}+a\dfrac{dt}{dx}\\\Rightarrow dv=du+tda+adt\\\Rightarrow dv=2+10\times 0.1+5\times 1\\\Rightarrow dv=8\ \text{m/s}$

The velocity after time has passed is $v+dv=(70\pm 8)\ \text{m/s}$.