A particle moves along the x axis. Its position is given by the equation
x = 1.9 + 2.5t − 3.7t2 with x in meters and t in seconds.

(a) Determine its position when it changes direction.
____m

(b) Determine its velocity when it returns to the position it had at t = 0? (Indicate the direction of the velocity with the sign of your answer.)
____m/s

Question

A particle moves along the x axis. Its position is given by the equation 
x = 1.9 + 2.5t − 3.7t2 with x in meters and t in seconds.

(a) Determine its position when it changes direction.
 ____m

(b) Determine its velocity when it returns to the position it had at t = 0? (Indicate the direction of the velocity with the sign of your answer.)
 ____m/s

anonymous · Answer

You can find when its direction will change by derivating x with respect to time so you get 2.5-7.4t which is the equation of velocity. When velocity is 0, the direction of motion changes. so at t= 2.5/7.4 its direction will change. if you put this number on x you get the position.

anonymous · Answer

for second question|dw:1315676788886:dw| we get this graph. In previous question we get velocity equation v=2.5-7.4t so at t=0 initial velocity is 2.5m/s. This is a linear equation as you see at the graph above. So when it returns to the position it had at t=0 its velocity will be -2.5 because the direction has changed.