Question

if
x = 2 Sin 2t
y = 4 Cos 2t
Then find speed
speed of the object

I.e. v=?​

Answer 1

Explanation:

The displacement equation of a particle is x=3 sin2t+4cos2t . The amplitude and maximum velocity will be respectively · 5,10 · 3,2 · 4,2 · 3, 4 · If A ...

Answer 2

Given

The x co-ordinate and y co-ordinate of a body varies with time and hence,it is a two dimensional motion.

We have, x = 2 Sin 2t

y = 4 Cos 2t

Concept

Since, distance is not a linear function of time,We have to solve the given question using instantaneous concept.That is using differentiation.

Calculation

Velocity along x axis

$v_x\:=\: \dfrac{dx}{dt}\:=\:\dfrac{d(2sin2t)}{dt} \\ \\ \implies \:v_x\:=\: 4cos2t$

Velocity along y-axis

$v_y\:=\: \dfrac{dy}{dt}\:=\:\dfrac{d(2Cos2t)}{dt} \\ \\ \implies \:v_y\:=\: -4sin2t$

Finding speed

Speed can be find by using vector law of addition.Here, velocity is along x-axis and -y-axis and therefore,they are perpendicular.

net speed

$= \:\sqrt{{(4cos2t)}^2\:+\:{(-4sin2t)}^2} \\ \\ \implies \: \sqrt{16} \\ \\ \implies \: speed\:=\:4\:unit\:s^{-1}$