Question

the displacement of a particle moving along x-axis is given by X = 18t + 5t.
calculate:
(i) the instantaneous velocity at t = 2s.
(ii) average velocity between t = 2 s and t = 3s.
(iii) instantaneous acceleration​

Answer 1

Given

The displacement of a particle moving along x-axis is given by

• x = 18t + 5t²

To Find

i. Instantaneous velocity at t = 2 s

ii. Average velocity b/w t = 2 s and t = 3 s

iii. Instantaneous acceleration

Solution

i.

$\rm v=\dfrac{dx}{dt}\\\\\implies \rm v=\dfrac{d}{dt}(18t+5t^2)\\\\\implies \rm v=18+10t$

Instantaneous Velocity at  t = 2 s is given by ,

$\implies \rm v=18+10(2)\\\\\implies \bf \pink{v=38\ m/s}\ \; \bigstar$

ii.

Average velocity is given by displacement per change in time

$\implies \rm A_{v}=\dfrac{x_2-x_1}{t_2-t_1}$

$\implies \rm A_v=\dfrac{\{18(3)+5(3)^2\}-\{18(2)+5(2)^2\}}{3-2}$

$\implies \rm A_v=\dfrac{\{54+45\}-\{36+20\}}{1}\\\\\implies \rm A_v=99-56\\\\\implies \bf \green{A_v=43\ m/s}\ \; \bigstar$

iii.

Instantaneous acceleration is given by ,

$\implies \rm a=\dfrac{dv}{dt}\\\\\implies \rm a=\dfrac{d}{dt}(18+10t)\\\\\implies \bf \blue{a=10\ m/s^2}\ \; \bigstar$