# Physics - Write an equation that describes the position x of a particle in relation to the time t?

A particle moves in a circle with a radius of 0.4 m, with a constant speed of 0.8 m/s.

Write an equation that gives x in relation to time t, supposing that in t=0, the particle is on the positive side of the x axis.

Can someone please explain the general equation for this type of problems?

### 1 Answer

- WhomeLv 71 month agoFavourite answer
A point on the rim of a wheel spinning with its axis at the origin casts a "shadow" on the x axis which is a sinusoidal function.

As the point is moving a distance equal to two radii every second, we know that its angular velocity ω = 2 rad/s

If we let the shadow be at its maximum excursion of 0.4 m at time zero, we are inclined to use a cosine function as cos0 = 1

the general equation would be

x = Acos(ωt + φ)

x = 0.4 cos(2t + φ)

where φ is the phase shift and in this case could be any value

-π/2 < φ < π/2 keeping the x value positive when t = 0