A particle moves on a curve in space, R(t), with constant speed. Show that it velocity and acceleration are?

Question

always perpendicular, no matter what the shape of the curve is.

Answer 1

Any component of acceleration in the direction of the particle will change its speed. Therefore, the acceleration must always be perpendicular to the instantaneous direction of travel, although it can vary in magnitude, which will vary the shape of the curve.

Answer 2

v= a(t) *i+b(t) j+c(t)*k with a^2+b^2+c^2 =constant
@= da/dt*i+db/dt*j+dc/dt k
and a*da/dt +b*db/dt+c*dc/dt =0 (x)
Take the dot product of v and @ which is precisely the expression (x)
so it is 0 and the vectors are perpendicular

Answer 3

Show that it velocity and acceleration are?............

...............................

Please take your time to rethink your question. Ask that question to yourself and think if you could find a answer to this rethorik masterpiece.