Question

A particle of mass moves under a force given bywhere and are unit vectors in the and directions. The particle is placed at the origin with an initial velocity After how much time will the particle first return to the origin

Answer 1

The elapsed time when the particle returns to the origin is determined from the ratio of initial velocity and acceleration of the particle.

Time of motion of the particle

The time of motion of the particle is calculated by applying Newton's second law of motion.

F = ma

F = m(v)/t

where;

• t is time of motion of the particle
• m is mass of the particle
• v is velocity of the particle

a = v - u/t

v = u + at

when the particle returns to the origin, direction of u, = negative.

final velocity = 0

0 = -u + at

at = u

t = u/a

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