The derivative of a sum is the sum of the derivatives of each term. Look at the x direction and y direction, separately. Those x and y's in the equation are confusing. they indicate the component directions of the displacemnt. I'll start you off with dr/dt in the x direction: d/dt(6t^3) =18t^2. Continue...XwakeriderX said:
Not quite. the acceleration is 14.4t^2 in the x direction and 36t in the ydirection. You have to look in each direction separately. That's what the 'hat' indicated in the original equation...x_hat is the displacement in the x direction, and y_hat is the displacement in the y direction. So you have to plug in t=5 for each component. You can't just add them because they are perpendicular. So what is the x component of acceleration and what is the y component of acceleration at t=5? And by the way, the acceleration has units of m/sec^2.XwakeriderX said:
Yes, that is exactly right! But now once you get that result for the acceleration, you then need to find the net force causing that acceleration. The net force is always in the direction of the acceleration. What famous law would you use to calculate the Force, once you know the mass and acceleration? (Note: I figure if the Sox win their remaining 16 games and the Yanks or Rays lose half of their remaining games , we're in!).XwakeriderX said:
Where'd you get the 10..the mass is given as 15 kg. Once you make that correction, you will end up with correct value of the x and y components of the net force (in units of Newtons), and then to get the resultant net force and direction, you can do that square root and tan theta thing you did for the acceleration. OR, you can calculate the net acceleration and direction as per your prior post, and then apply Newton 2 directly to that result to get the force and direction, which must be in the same direction as the acceleration. Either way is OK.XwakeriderX said:
Looks good, nice effort!XwakeriderX said:
It was my pleasure. Wecome to PF! There are experts on this Forum in every area of science and math you can imagine, who are more than willing to assist as long as you show your relevant equations and an attempt at a solution. Come on back now, you hear?XwakeriderX said:
The magnitude and direction of the net force vector refers to the overall strength and direction of the combined forces acting on an object.
The magnitude of the net force vector can be calculated by adding together all of the individual forces acting on an object, taking into account their direction and magnitude.
A positive net force vector indicates that the combined forces acting on an object are in the same direction, resulting in an overall increase in speed or acceleration.
A negative net force vector indicates that the combined forces acting on an object are in opposite directions, resulting in an overall decrease in speed or acceleration.
The direction of the net force vector determines the direction of an object's motion. An object will move in the same direction as the net force vector, following the path of least resistance.