Question

Sketch the position, velocity and acceleration vs. time graphs for a ball that rolls up an inclined plane, with an initial velocity small enough that the ball will come to a stop for a fraction of a second and then return to the base of the inclined plane.

Answer 1

position as in height ?

Answer 2

meters yes, it doesnt' have to be exact just a rough sketch, but I don't know how to because it goes up the plan thenn back down

Answer 3

ok lets start with acceleration.
a ball rolling up a ramp has no upward acceleration only the force of gravity pushing it back down to the ground
the force of gravity has a acceleration of -9.8 m/s^2

the graph is a straight line (y= -9.8)

Answer 4

velocity is the antiderivative of acceleration
v(t) = -9.8t + v_o
where v_o is the initial velocity of the ball

graph will be a neg sloped line with y-intercept of initial velocity

Answer 5

ok so don't account for the upward motion of the ball

Answer 6

the upward motion is accounted for with the initial velocity

Answer 7

ok

Answer 8

position is antiderivative of velocity

h(t) = -4.9t^2 + (v_o)t + h_o

initial height is 0

graph is a parabola
y = -4.9t^2 + (v_o)t
starting at origin, then going up to vertex, then down back to x_axis