How Does a Particle's Motion Change Direction and Velocity Over Time?

[mooneh]

a particle moves along the x-axis. its position is given by the equation x=2+3t-4t^2

determine its position when it changes direction.
and its velocity when it returns to the position it had at t=0

 

[learningphysics]

Give it a shot yourself. we'll help you along.

 

[ogb p]

The position of the particle when it changes direction can be determined by setting the velocity equation equal to zero, as this is the point where the particle changes direction. In this case, the velocity equation is v=3-8t. Setting this equal to zero gives us t=3/8. Plugging this value into the position equation, we get x= 2+3(3/8)-4(3/8)^2 = 2+9/8-9/16 = 49/16. So, the position of the particle when it changes direction is 49/16 units on the x-axis.

To determine the velocity when the particle returns to its initial position at t=0, we can simply plug in t=0 into the velocity equation. This gives us v=3-8(0) = 3 units per second. This means that the particle has a velocity of 3 units per second when it returns to its initial position at t=0.