Accelerated vertical motion is motion straight up or down with constant acceleration from gravity, usually about 9.81 m/s^2 downward. In Principles of Physics I, it shows up in dropped objects, thrown balls, and vertical parts of projectile motion.
Accelerated vertical motion is the up-or-down motion of an object when gravity is the only significant force acting on it. In Principles of Physics I, that means the object has a constant acceleration of about 9.81 m/s^2 downward, no matter whether it is moving upward, downward, or momentarily stopping at the top of its path.
The easiest way to think about it is this: velocity can change direction, but acceleration from gravity keeps pointing downward the whole time. If you throw a ball straight up, its velocity is upward at first, then gravity slows it down until the velocity reaches zero at the top. Right after that, the same downward acceleration makes it speed up as it falls back down.
This is why a ball thrown up and a ball dropped from rest can be analyzed with the same kinematic equations. The difference is the starting condition, not the acceleration. A dropped object starts with initial velocity 0, while a tossed object may start with an upward or downward initial velocity. That initial velocity changes the height it reaches and the time it spends in the air, but not the value of the acceleration.
A common sign convention in physics classes is to choose upward as positive. If you do that, the acceleration due to gravity is negative, usually written as a = -9.81 m/s^2. If you choose downward as positive, then the same gravitational acceleration is positive. The math works either way as long as you stay consistent with your signs.
Air resistance is usually ignored in this topic. That simplification lets you treat the motion as uniformly accelerated, which means the equations stay clean and predictable. It also explains why, in ideal problems, two objects of different mass fall with the same acceleration. The mass does not change the free-fall acceleration when air resistance is neglected.
Accelerated vertical motion is the backbone of vertical kinematics in Principles of Physics I. Once you can identify that gravity is the only acceleration acting, you can solve for height, time, velocity, and displacement using one set of equations instead of guessing from the picture.
It also gives you the vertical half of projectile motion. When a ball is launched at an angle, the horizontal and vertical motions are treated separately. The vertical component is still accelerated by gravity, so this concept is what lets you find the time of flight, the maximum height, and the landing speed in a projectile problem.
This term shows up any time a problem asks about a dropped object, a tossed object, an elevator-like vertical path, or the top of a projectile's arc. If you can identify the motion as vertically accelerated, you know which variable changes steadily and which one reaches zero at the peak. That is the difference between setting up the problem correctly and getting lost in the algebra.
It also builds a major habit in physics: choosing a sign convention and sticking to it. Many mistakes in kinematics come from mixing up velocity direction, acceleration direction, and what positive means. This topic forces you to keep those pieces separate, which pays off in later work with forces, energy, and momentum.
Keep studying Principles of Physics I Unit 3
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view galleryGravity
Gravity is the force that causes the constant downward acceleration in accelerated vertical motion. In ideal problems, gravity is the only force you keep, which is why the acceleration stays the same from start to finish. The value near Earth's surface is about 9.81 m/s^2, and that number drives the vertical equations you use.
Free Fall
Free fall is the special case of accelerated vertical motion where gravity is the only force acting on the object. A dropped stone, a ball tossed upward, and an object at the top of its path are all in free fall if air resistance is ignored. The motion is still accelerated even when the object is moving upward more slowly.
Kinematic Equations
The kinematic equations are the tools you use to solve accelerated vertical motion problems. They connect displacement, initial velocity, final velocity, acceleration, and time under constant acceleration. In vertical motion, you plug in the gravitational acceleration and use your sign convention to find unknowns like maximum height or time in the air.
Maximum Height
Maximum height is the point where the vertical velocity becomes zero for an instant. That does not mean acceleration stops, because gravity is still pulling downward. This makes it a useful checkpoint in problems involving a thrown object, since you can solve for the time to the peak and then use symmetry or kinematics for the rest of the motion.
A problem set or quiz question usually asks you to identify the vertical direction, choose a sign convention, and then use a kinematic equation to solve for an unknown. You might be given a launch speed, a drop height, or a time and asked for the peak height, impact velocity, or total flight time. The main move is to treat the vertical path as constant acceleration under gravity, not as a changing acceleration problem.
If the object is part of projectile motion, split the motion into x and y components before doing any math. The vertical component uses accelerated vertical motion, while the horizontal component is separate. A good check is whether the velocity at the top should be zero only in the vertical direction, not the whole motion.
Horizontal motion in projectile problems is usually constant velocity, not accelerated motion, if air resistance is ignored. Accelerated vertical motion changes because gravity acts downward, while horizontal motion does not have that same acceleration. Students often mix them up because both happen at the same time, but they are solved with different equations and different acceleration values.
Accelerated vertical motion is straight-up or straight-down motion with constant acceleration from gravity, usually about 9.81 m/s^2 downward.
The acceleration stays the same even when the object is moving upward, stopping at the top, or falling back down.
Your initial velocity changes the height reached and the time in the air, but it does not change gravity's acceleration.
Pick a sign convention at the start and use it consistently, because a sign mistake can flip the whole problem.
In projectile motion, the vertical part uses accelerated vertical motion while the horizontal part is handled separately.
It is motion straight up or down with constant acceleration caused by gravity. In most problems, that acceleration is about 9.81 m/s^2 downward, whether the object is rising, falling, or at the peak of its path. You use it to analyze dropped objects, thrown objects, and the vertical part of projectile motion.
Not exactly, but they are closely related. Free fall is the special case where gravity is the only force acting, which includes objects dropped from rest and objects thrown upward or downward if air resistance is ignored. Accelerated vertical motion is the broader idea of any vertical motion with constant gravitational acceleration.
It is negative only if you choose upward as positive on your coordinate system. Gravity still points downward the whole time, so its acceleration has the opposite sign from your chosen positive direction. If you choose downward as positive, the same gravitational acceleration becomes positive instead.
Start by choosing a positive direction, then identify the known values: initial velocity, acceleration, displacement, or time. After that, use a kinematic equation that matches the unknown you need. A common mistake is mixing up velocity and acceleration, especially at the top of the motion where velocity is zero but acceleration is not.