Question

A bird files for 4s with a velocity of $|t-2|m/s$ in a straight line, where t is time in seconds. It covers a distance of:

• A. 2m
• B. 4m
• C. 6m
• D. 0m

Answer 1

The correct option is B 4m

The velocity of the bird is a function of time t as $v=(t-2)m/s$

Now. we know that

$Distance=speed\times time$

We also know that distance will always be positive. So, for the first 2 seconds, the velocity dependent on t will be given as $(2-t)m/s$ and for the next 2 seconds, it will be $(t-2)m/s$

Hence, we get

$v=\frac{dx}{dt}$

$dx=vdt$

${\int }_0^{x}dx={\int }_0^{4}vdt$

${\int }_0^{x}dx={\int }_0^2(2-t)dt+{\int }_2^4(t-2)dt$

$x={\int }_0^{2}2dt-{\int }_0^{2}tdt+{\int }_2^{4}tdt-{\int }_2^{4}2dt$

$x=2t{|}_0^2-\frac{t^2}{2}{|}_0^2+\frac{t^2}{2}{|}_2^4-2t{|}_2^4$

$x=4-2+8-2-8+4$

$x=4m$