CHAPTER 21. MOTION IN ONE DIMENSION 21.6
is now travelling at a constant velocity, thus the velocity vs. time graph
will be a horizontal line during this stage. We can now draw the graphs:
So our velocity vs. time graph looks like this one below. Because
we haven’t been given any values on the vertical axis of the displace-
ment vs. time graph, we cannot figure out what the exact gradients are
and therefore what the values of the velocities are. In this type of ques-
tion it is just important to show whether velocities are positive or nega-
tive, increasing, decreasing or constant.0 1 2 3 4 5 6~v(m·s−^1 )t(s)Once we have the velocity vs. time graph its much easier to get the
acceleration vs. time graph as we know that the gradient of a velocity
vs. time graph is the just the acceleration.Step 5:Acceleration vs. time graph for 0 – 2 seconds
For the first 2 seconds the velocity vs. time graph is horizontal and has
a value of zero, thus it has a gradient of zero and there is no acceler-
ation during this time. (This makes sense because we know from the
displacement time graph that the object is stationary during this time,
so it can’t be accelerating).Step 6:Acceleration vs. time graph for 2 – 4 seconds
For the next 2 seconds the velocity vs. time graph has a positive gradi-
ent. This gradient is not changing (i.e. its constant) throughout these 2
seconds so there must be a constant positive acceleration.Step 7:Acceleration vs. time graph for 4 – 6 seconds
For the final 2 seconds the object is travelling with a constant velocity.
During this time the gradient of the velocity vs. time graph is once again
zero, and thus the object is not accelerating. The acceleration vs. time
graph looks like this:
a(m·s−^2 )0 2 4 6 t(s)Step 8:A description of the object’s motionPhysics: Mechanics 419