Using your equations: x(3)=16-12*3+2*9=16-36+18=-2 and v(3)=0.Gjmdp said:Homework Statement
Calculate velocity. x=position. t=time
Homework Equations
x=16-12t+2(t^2)
The Attempt at a Solution
Derivative of x: v=4t-12
Ok let's try:
Equation of x: x=16-12t+2(t^2)
Equation of v: v=4t-12
With the equation of x: x(3)=2 then v(3)=3/2.
Ok, but with the equation of v: v(3)=0.
There are different results! Why?
What am I doing wrong?
So x(3)=-2 in t=3.Samy_A said:Using your equations: x(3)=16-12*3+2*9=16-36+18=-2 and v(3)=0.
How do you get v(3)=3/2?
You are computing two different quantities.Gjmdp said:So x(3)=-2 in t=3.
v=x/t
v(3)=-2/3
I was wrong.
But it keep being different
v=0: v=-2/3
How did you get -13?Gjmdp said:-13/3 is the average speed from t=0 to t=3 OK thanks a lot.
v is not equal to x/t. This is only correct if x =0 at t = 0 (which in your problem it is not) and if v is constant (which in your problem it is not).Gjmdp said:So x(3)=-2 in t=3.
v=x/t
v(3)=-2/3
Sorry, I was wrong.
But it keep being different
v(3)=0: v(3)=-2/3
Velocity is defined as the rate of change of an object's position over time. Different equations may use different variables or assumptions, leading to different values for velocity.
Average velocity is calculated by dividing the total displacement by the total time taken, while instantaneous velocity is the velocity at a specific moment in time. Average velocity is an overall measure, while instantaneous velocity provides information about an object's velocity at a specific point.
Velocity is a vector quantity that includes both magnitude (speed) and direction. Some equations may only need to consider the magnitude, so they use the term speed instead of velocity.
Acceleration is the rate of change of velocity over time. If an object experiences acceleration, its velocity will change. If the acceleration is in the same direction as the velocity, the object's speed will increase. If the acceleration is in the opposite direction, the object's speed will decrease.
Velocity involves both magnitude (speed) and direction, making it a vector quantity. Representing velocity as a vector allows us to easily calculate its components in different directions and analyze the motion of an object in a more comprehensive manner.