Physics
Objects accelerating on a ramp
Four different scenarios
Scenario 1: Object on ramp moving down a ramp away from the reference point
VISUAL CLUES:
Draw tangent lines. The slopes of the tangent
lines = velocities. Start at the initial time and
work your way through time.
Construct tangent lines with your hand or ruler.
Think about what they look like as you create
them.
In this case the slope of the tangent line is
increasing and becoming more and more steep in
the positive direction. The initial velocity (Vi) =
0 m/s and the cart starts at the reference point (Xi)
= 0 m, too
Does this graph confirm what we saw on with the
tangent lines? The velocity starts slow and
becomes a bigger and bigger positive number as
the object rolls down the ramp away from the
reference point.
This vt shows a linearity. The slope on the
velocity-time graph = acceleration. This is a
positive acceleration because the slope is positive.
It is constant because of the linearity.
acceleration (m/s^2)
1.5
1
time (sec)
0
-1
-1.5
0
1
2
Ramp Scenarios, adg, p. 1, 2/16/2016
3
4
5
Scenario 2: Object on ramp moving up a ramp towards the reference point
VISUAL CLUES:
To get the cart moving up the incline plane, you
need to give it an initial velocity. Consequently,
a Vi exists (Vi ≠ 0 m/s). The cart is starting
away from the reference point so the initial
position of the cart, Xi ≠ 0 m.
But what happens to the cart’s velocity as it goes
up the incline? Gravity pulls on the cart and
slows it down.
Because the object is going back toward the
reference point, these velocities are negative
(remember this from the previous unit?)
Check the slopes of the tangent lines. It begins
as a fairly steep negative slope but becomes
more and more horizontal with time. This
means the velocity is becoming less negative as
it approaches zero. The velocity becomes zero
as the cart is pulled to a stop on the ramp.
The velocity-time graph confirms this. The
slope (acceleration) is positive as the velocity is
becoming less and less negative. It starts out at
some Vi that is negative. This initial velocity is
based on how strongly it is pushed up the incline
and gets more and more horizontal.
acceleration (m/s^2)
1.5
1
Can you see the slope of the vt is
positive? This means the acceleration
is positive. It is a constant value.
time (seconds)
0
-1
-1.5
0
1
2
Ramp Scenarios, adg, p. 2, 2/16/2016
3
4
5
Scenario 3: An object moving down a ramp moving toward the reference point
VISUAL CLUES:
The cart starts from rest and gains speeds as
gravity pulls it down the incline plane.
However this velocity is negative as it is
traveling toward the reference point.
Look at the slopes of the tangent lines. It
starts out somewhat horizontal (Vi = 0 m/s)
and becomes steeper and steeper (steeper and
steeper negative). Verify this by using your
ruler or hand to make the tangent lines.
Because it is starting away from the reference
point, the initial position, Xi ≠ 0 m.
So, the velocity time graph starts out at zero
and becomes more negative. This creates a
slope here but in the negative direction. This
means the acceleration is constant but a
negative value!
acceleration (m/s^2)
1.5
1
time (seconds)
0
-1
-1.5
0
1
2
Ramp Scenarios, adg, p. 3, 2/16/2016
3
4
5
Scenario 4: An object moving up a ramp moving away from the reference point
VISUAL CLUES:
The physics cart is moving away from the reference point (Xi =
0 m). Consequently, slopes of the tangent lines are positive.
However, it is going up the incline plane.
So, the initial velocity must be some non-zero value (Vi ≠ 0
m/s) as to push the cart up the plane. Gravity acts to slow the
cart down. The slopes of the tangent lines must be getting
smaller and smaller with time. Check it out by drawing tangent
lines with your hand or ruler. The tangent lines become more
and more horizontal in nature.
The initial velocity is high as seen in the vt graph as discussed
above. The velocity is continually decreasing because of pull
of gravity and approaches 0 m/s.
We see a linearity on the vt graph and the slope here represents
a constant acceleration. It will be a negative slope, a =
negative.
acceleration (m/s^2)
1.5
1
time (seconds)
0
-1
-1.5
0
1
2
Ramp Scenarios, adg, p. 4, 2/16/2016
3
4
5
Bonus Scenario 5: Object moving up a ramp away from a reference point and then it moves back down
the ramp away towards the reference point. All of this is one complete motion.
OK, can you guess the shapes of the graphs you will get?? Think about it and refer to the earlier
scenarios.
Ramp Scenarios, adg, p. 5, 2/16/2016
Why is the previous scenario so important??
Because this is the types of graphs we get when we throw an object straight up and allow it to come
down:
For example check this out:
Ramp Scenarios, adg, p. 6, 2/16/2016