Question #123135

2. (a) A particle P moves along the x-axis with constant acceleration a in the positive x-direction. Initially

P is at the origin and is moving with velocity u in the positive x-direction. Show that the velocity v

and displacement x of P at time t are given by

v = u + at, x = ut +

1

2

at2

,

and deduce that

v

2 = u

2 + 2ax.

(b) The trajectory of a charged particle moving in a magnetic field is given by

r = b cos (Ωt)i + b sin (Ωt)j + ctk,

where b, Ω and c are positive constants. Show that the particle moves with constant speed and find the

magnitude of its acceleration.

P is at the origin and is moving with velocity u in the positive x-direction. Show that the velocity v

and displacement x of P at time t are given by

v = u + at, x = ut +

1

2

at2

,

and deduce that

v

2 = u

2 + 2ax.

(b) The trajectory of a charged particle moving in a magnetic field is given by

r = b cos (Ωt)i + b sin (Ωt)j + ctk,

where b, Ω and c are positive constants. Show that the particle moves with constant speed and find the

magnitude of its acceleration.

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