Question

Bird flies with velocity (t-2)ms1 . calculate the displacement and distance covered by the bird in 4s

Answer 1

distance is 2 metres

Answer 2

Answer: The displacement covered by the bird is zero and distance is 4 m in 4 sec.

Explanation:

Given that,

Velocity $v = (t-2)m/s$

We know that,

The distance covered by the bird is

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

$dx = vdt$

On integrating

$\int_{0}^{x}dx=\int_{0}^{4}v\ dt$

$x = \int_{0}^{2}(2-t)dt+\int_{2}^{4}(t-2)dt$

$x = (2t-\dfrac{t^2}{2})_{0}^{2}+(\dfrac{t^2}{2}-2t)_{2}^{4}$

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

$x = 4\ m$

The displacement covered by the bird is

$x(t)= \dfrac{t^2}{2}-2t+c$

At t = 0, X(0)= 0

Therefore, c = 0

$x(t)= \dfrac{t^2}{2}-2t$

At t = 4 s

$x(4)= 0$

Hence, The displacement covered by the bird is zero and distance is 4 m in 4 sec.