The discussion focuses on calculating the speed and direction of an object defined by parametric equations at a specific time, t = 3 seconds. The coordinates are given as x = 25t and y = 20t - 5t². The velocity components are derived as dx/dt = 25 and dy/dt = 20 - 10t, leading to the velocity vector v. At t = 3 seconds, the speed is calculated using the formula v = √((dy/dt)² + (dx/dt)²), resulting in a definitive speed and direction for the object.
PREREQUISITESStudents studying physics, particularly those focusing on motion in two dimensions, as well as educators looking for examples of parametric equations in action.
What you are calling dx and dy are reallyMushroom79 said:Homework Statement
An object moves so it's coordinates at the time t is given by the relationships
x = 25t
y = 20t-5t^2
What is the object's speed and direction at 3 sec?
t = 3 sec
Homework Equations
v = √(dy/dt)^2 / (dx/dt)^2
Pythagoras theorem
The Attempt at a Solution
dx=25
dy=20-10t
I'm not sure how I should use this by combining the two formulas above.
Redbelly98 said:What you are calling dx and dy are really
\frac{dx}{dt} \text{ and } \frac{dy}{dt}
which is the same as vx and vy. So you have found the two components of the velocity vector v -- or at least you'll have them once you plug the time value into your expression. So as a start, figure out what the values of vx and vy are, using the expressions you got.