Question

In 2-D motion body moves

x = 5sin10t aur y=5cos10t

then it's speed at t = 2sec nd t = 5sec​

Answer 1

AnswEr :

The speed of particle is 50m/s.

ExplanaTion :

Given,

• A particle is moving in 2-D motion.

• x = 5 sin(10t) and y = 5 cos(10t)

• Speed of particle at t = 2sec and t = 5sec.

Solution,

Velocity of the particle along the direction of x-axis is

$\frac{dx}{dt}$

Velocity of the particle along the direction of y-axis is

$\frac{dy}{dt}$

=> Here,

Velocity in x-direction

$v(x) = \frac{d(x)}{dt}$

$v(x) = \frac{d(sin10t)}{dt}$

After, differentiating, we get

$v(x) = 5 \cos(10t) \times 10$

$v(x) = 50 \cos(10t)$

Similarly,

$v(y) = \frac{d(y)}{dt}$

$v(y) = \frac{d(5 \cos(10t) }{dt}$

By, differentiating we get ,

$v(y) = 5 \sin(10t) \times 10$

$v(y) = 50 \sin(10t)$

We know that,

speed = magnitude of velocity,

here, magnitude of velocity

$|v| = \sqrt{ {v(x)}^{2} + {v(y)}^{2} }$

$|v| = \sqrt{ {(50 \: \cos(10t))}^{2} + {(50 \sin(10t)) }^{2} }$

$|v| = \sqrt{ {50}^{2}( {sin}^{2} 10t + {cos}^{2} 10t) }$

$|v| = \sqrt{ {50}^{2} + (1)}$

$|v| = \sqrt{ {(50)}^{2} }$

$|v| = 50mps$

therefore, the speed of particle , which is equal to the magnitude of velocity is 50m/s