Question

a particle starts its motion from origin with velocity 2i cap m/s and moves in xy plane with uniform acceleration 1i cap+ 3j cap a) what will be the value of y coordinate when value of x coordinate is 30m b) what will be its speed at this time??​

Answer 1

Given:

A particle starts its motion from origin with velocity 2i cap m/s and moves in xy plane with uniform acceleration 1i cap+ 3j cap.

To find:

• Value of Y coordinate at that time?
• Speed at that time?

Calculation:

Net acceleration is :

$\rm a = \sqrt{ {1}^{2} + {3}^{2} } = \sqrt{10} \: m {s}^{ - 2}$

Now, applying 3rd equation of kinematics:

$\rm {v}^{2} = {u}^{2} + 2as$

$\rm \implies {v}^{2} = {(2)}^{2} + (2 \times \sqrt{10} \times 30)$

$\rm \implies {v}^{2} = 4 +60 \sqrt{10}$

$\rm \implies {v}^{2} = 193.7$

$\rm \implies v = 13.9 \: m {s}^{ - 1}$

_______________________________

$\rm \: v = u + at$

$\rm \implies \: 13.9 = 2+ t \sqrt{10}$

$\rm \implies \: t \sqrt{10} = 11.9$

$\rm \implies \: t =3.76 \: sec$

So, y coordinate:

$\rm \: y = u_{y}(t) + \dfrac{1}{2} a_{y} {t}^{2}$

$\rm \implies\: y =0 + \dfrac{1}{2} \times 3 \times {(3.76)}^{2}$

$\rm \implies\: y = 21.2 \: m$

So, y coordinate at that time is 21.2 metre.