Question
Suppose a cart slides from rest down a frictionless track tilted at some angle ?. Assume:
- Down the incline is positive
- The origin is at the top of the track.
a) If you plot displacement vs. time for the cart, the graph appears as a straight line with negative slope starting at the origin a parabola, open upward a parabola, open downward a straight line along the x (time) axis a straight line parallel to the x (time) axis and below the x-axis a straight line with negative slope, starting from a point on the positive y-axis o a straight line along the y-axis o a straight line parallel to the x (time) axis and above the x-axis a straight line with positive slope starting at the origin a straight line with positive slope, starting from a point on the positive y-axis b) If you plot velocity vs. time for the cart, the graph appears as o a straight line parallel to the x (time) axis and below the x-axis a straight line with positive slope starting at the origin o a straight line along the y-axis a straight line with positive slope, starting from a point on the positive y-axis a parabola, open downward o a parabola, open upward a straight line with negative slope starting at the origin o a straight line parallel to the x (time) axis and above the x-axis a straight line with negative slope, starting from a point on the positive y-axis a straight line along the x ( time) axis b) If you plot acceleration vs. time for the cart, the graph appears as O a parabola, open downward o a straight line parallel to the x (time) axis and below the x-axis o a straight line along the y-axis a straight line with positive slope starting at the origin a straight line with positive slope, starting from a point on the positive y-axis a straight line with negative slope, starting from a point on the positive y-axis o a straight line along the x (time) axis o a straight line parallel to the x (time) axis and above the x-axis a straight line with negative slope starting at the origin o a parabola, open upward
Explanation / Answer
a) Here a = g*sin(theta) =constant
u = 0
Then S = ut + 0.5*a*t^2
S = constant*t^2
So, The graph will be parabola, open and upwards
b) Now v = u + at
As u = 0, v = constant*t
The graph will be a straight line with positive slope starting at the origin.
c) a = g*sin(theta) =constant
a straight line parallel to the x (time) axis and above the x-axis
