Question

A particle moves in a 2D motion such that its position depends on time as -
$x = 4 {t}^{2} + 2t + 3$
$y = 5t + 7$
find the velocity of the particle at t = 2s​

Answer 1

A particle moves in a two dimensional motion such that its position depends on time as -

x = 4t² + 2t + 3

y = 5t + 7

To find : the velocity of the particle at t = 2sec

solution :

velocity of the Particle along x - axis.

differentiating x = 4t² + 2t + 3, with respect to time we get,

dx/dt = v_x = d(4t² + 2t + 3)/dt = 8t + 2

at t = 2 sec, v_x = 8 (2) + 2 = 18 m/s

velocity of the particle along y - axis

differentiating y = 5t + 7, with respect to time we get,

dy/dt = v_y = d(5t + 7)/dt = 5

at t = 2sec, v_y = 5 m/s

so the vector form of velocity of the particle at t = 2sec is , v = 18 i + 5 j

magnetic of velocity of particle at t = 2 sec, |v| = √{18² + 5²} = 18.68 m/s

Therefore the magnetic of velocity of the particle at t = 2sec is 18.68 m/s .