# Calculus - kinematics

• Apr 2nd 2009, 09:46 AM
acc100jt
Calculus - kinematics
Hi, i have a question regarding kinematics.

I know that acceleration is the rate of change of velocity.
and if a<0, it is known as deceleration.

Consider a particle moving in a straight line and the velocity is given by
v(t)=1-t, a simple linear function,

For 0<t<1, acceleration is -ve so the particle is decelerating.

At t=1, v=0, so the particle is at rest.

Then for t>1, the particle change direction and increases its speed.

However, for t>1, acceleration, dv/dt is still -ve, but it is not decelerating for t>1 right? It should be accelerating!

Thanks!!
• Apr 2nd 2009, 10:34 AM
acc100jt
can I say that for the reverse direction, negative acceleration actually means the speed is increasing, whereby positive acceleration means deceleration?
• Apr 3rd 2009, 06:42 PM
mr fantastic
Quote:

Originally Posted by acc100jt
can I say that for the reverse direction, negative acceleration actually means the speed is increasing, whereby positive acceleration means deceleration?

You have to define the positive and negative direction. Then:

If the object is moving in the positive direction and has negative acceleration then it will be slowing down.

If the object is moving in the negative direction and has positive acceleration then it will be slowing down.

If the object is moving in the positive direction and has positive acceleration then it will be speeding up.

If the object is moving in the negative direction and has negative acceleration then it will be speeding up.