Question

The speed of a particle is given by u=at.where a is constant.the displacement in the first 4 seconds is given by. No SPAM. I NEED STEP WISE AND CLEAR EXPLANATION.

Answer 1

Answer

• Displacement = 8a m

Given

• The speed of a particle is given by u = at , where a is constant

To Find

• Displacement in first 4 s

Concept Used

$\bigstar \;\; \bf u=\dfrac{dx}{dt}$

Solution

$\rm u=at\\\\\implies \rm \dfrac{dx}{dt}=at\\\\\implies \rm dx=at.dt\\\\\rm Integrating\ on\ both\ sides\ ,we\ get,\\\\\implies \rm x=\int at.dt\\\\\implies \rm x=a\int t.dt\ [\; Since\ a\ is\ constant\ ]\\\\\implies \rm x=a.\dfrac{t^2}{2}\\\\\rm Since,we\ need\ to\ find\ displacement\ in\ first\ 4\ seconds.\\\\\implies \rm x=a.\dfrac{t^2}{2}\bigg]_0^4\\\\\implies \rm x=\dfrac{a}{2}(4^2)\\\\\implies \rm x=\dfrac{16a}{2}\\\\\implies \rm x=8a\ m$

So , Displacement in the first 4 seconds is 8a meters