Constant velocity & constant acceletation question?

Question

Can anyone help me solve this question? Thanks a lot for your help!

How can an object in uniform circular motion be moving at a constant speed and at the same time be constantly accelerating? For this same object, can we apply the following equations of motion:

v(final) = v(initial) + at
d(final) = d(initial) + v(initial) t + 1/2 at2 ?

Answer 1

When an object is in uniform circular motion, it has a constant acceleration and a constant speed.

The reason why there is a constant acceleration is due to the fact the velocity vector is changing direction. A simple proof of this is, when you swing a ball on a rope at a constant speed (constant period), you feel a tension in the rope. This tension is the centripetal force towards the center axis. When an object is subjected to a constant net force, a constant acceleration will result.

a=(v^2)/r where 'a' is the centripetal acceleration

Acceleration is a Vector (Has a magnitude & direction)

Velocity is a Vector (Has a magnitude & direction)
Speed is a Scalar (Has a magnitude but no direction)

Answer 2

You are confusing speed and velocity. Acceleration is the rate of change of *velocity* not speed. Velocity includes direction, so a change in velocity could mean a change in direction. Speed is a scalar quantity equal to the magnitude of the velocity vector. The equations you quote are scalar equations for linear motion only. There are equivalent vector equations; they look the same, but the quantities are vectors and the calculations more complex. See http://en.wikipedia.org/wiki/Acceleration

Answer 3

no, these equations are for linear motion

circular motion involves the change in the direction of the velocity even if the magnitude is constant, thus a non-zero acceleration

the main trick here is to think of velocity as a VECTOR

Answer 4

the object is moving at a constant speed (not acceleration) in a circular path
the constant acceleration is towards the center of the circle, it is caused by the centripetal force acting on the object

................v (tangent to circle)
............ <-----O.._
.............. /....|_|.......\
.........../...........|..F(centripetal)
..........|............\/..........|
...........\...................../
..............\.....___... /