Speed and Velocity question

In summary, the conversation discusses a horizontal projectile problem off a building. The participants question if the speed of an object is equal to v=a*t or v=|v| (magnitude), and provide the problem statement of Velocity = √(v_0^2 + g^2(2h/g)) positive below x axis and t = √(2h/g). It is clarified that v=at is only true for constant acceleration and zero initial velocity, and that v and |v| are different objects. Finally, the correct equation for speed is stated to be v = g√(2h/g), with units in g and h. The participants are asked to refer to a previous thread for further clarification.
  • #1
MathHelpa
4
0
This is a horizontal projectile problem off a building.

Is the speed of an object equal to:

##v=a*t##
or
##v = |v|## (magnitude)

Current problem:
##Velocity = √(v_0^2 + g^2(2h/g)) positive below x axis##

##t = √(2h/g)##

so is the speed suppose to be ##v = g√(2h/g) m/s##

or is it suppose to be

##|v| = √(v_o^2 + g^2(2h/g)) m/s##
 
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  • #2
v=at is true only if the acceleration is constant and the initial velocity is zero, it is not true in your case. You can use it for one velocity component (but not the full velocity) here.

v and |v| are different objects (vector and scalar), you cannot compare them with an equal sign.

v = g√(2h/g) m/s
The "m/s" there does not make sense. The units are in g and h.

or is it suppose to be
Please post the full problem statement, if you have questions how to interpret it.
 
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What is the difference between speed and velocity?

The main difference between speed and velocity is that speed is a scalar quantity that only considers the magnitude of an object's motion, while velocity is a vector quantity that takes into account both the magnitude and direction of an object's motion. In other words, speed tells us how fast an object is moving, while velocity tells us how fast and in what direction an object is moving.

How are speed and velocity measured?

Speed is typically measured in units of distance per time, such as meters per second (m/s) or miles per hour (mph). Velocity, on the other hand, is measured in units of distance per time in a specific direction, such as meters per second east (m/s east) or miles per hour north (mph north). Both speed and velocity can be measured using tools like speedometers or GPS devices.

Can an object have a constant speed but changing velocity?

Yes, an object can have a constant speed but changing velocity. This occurs when the object is moving in a circular path at a constant speed, but its direction is constantly changing. Since velocity takes into account the direction of an object's motion, a change in direction would result in a change in velocity even if the speed remains constant.

How does acceleration relate to speed and velocity?

Acceleration is the rate of change of an object's velocity over time. This means that if an object is accelerating, its speed or direction (or both) is changing. In other words, acceleration can cause a change in velocity, which in turn can cause a change in speed. However, if an object has a constant velocity, it is not accelerating, even if its speed is changing.

What are some real-life applications of speed and velocity?

Speed and velocity are used in various fields of science, engineering, and everyday life. For example, in physics, they are used to study the motion of objects and the effects of forces on those objects. In sports, speed and velocity are important for measuring and improving athletic performance. In transportation, they are used to calculate travel times and optimize routes. In weather forecasting, they are used to track the movement of storms and predict their paths. In short, speed and velocity play a crucial role in understanding and navigating the world around us.

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