Question

1. How would you expect an instantaneous acceleration vs. time graph to look for a cart moving with a constant

acceleration? With a uniformly increasing acceleration? With a uniformly decreasing acceleration? Make a rough
sketch of the graph for each possibility and explain your reasoning. To make the comparison easier, it is useful to
draw these graphs next to each other. Remember to assign labels and units to your axes. Write down an equation
for each graph. Explain what the symbols in each of the equations mean. What quantities in these equations can
you determine from your graph?
2. Write down the relationship between the acceleration and the velocity of the cart. Use that relationship to
construct an instantaneous velocity versus time graph just below each of your acceleration versus time graphs
from question 1, with the same scale for each time axis. Write down an equation for each graph. Explain what the
symbols in each of the equations mean. What quantities in these equations can you determine from your graph?
3. Write down the relationship between the velocity and the position of the cart. Use that relationship to construct a
position versus time graph just below each of your velocity versus time graphs from question 2, with the same
scale for each time axis. Write down an equation for each graph. Explain what the symbols in each of the
equations mean. What quantities in these equations can you determine from your graph?

Answer 1

a=0 v = v₀ + a t

a=0 line is horizontal

Step-by-step explanation:

1, In a graph of acceleration vs. time, we have lines, when the line is horizontal it is zero, when the line has a positive slope the increasing accelerations and when the slope is negative the decreasing acceleration

2, speed and relationship of a car is given by

v = v₀ + a t

where vo is the initial velocity, a is the acceleration and tel time

in this case I will calcograph velocity vs. time the constant acceleration is a straight line.

In general from the graph we can find the initial velocity with the cut at that x and the acceleration of the car with the slope