Solving Calc-Based Physics Problems: Object Position and Velocity at t=2s

[possum30540]

Homework Statement

An objects position as a function of time is given by r=12ti+(15t-5.0t^2)jm, where t is time in seconds. A: what is the onject's position at t=2 s. B what is its average velocity in the interval from t=o to t=2.0s.C: what is its instantaneous velocity at t=2?

Homework Equations

Derivative:12i+(15-10t)

V=change in r/change t

The Attempt at a Solution

A: simply plug 2 in for t in the original equation
B:take the derivative of the problem and plug in 2 for t
C: Dont really know . . .

 

[Doc Al]

A: simply plug 2 in for t in the original equation

OK.

B:take the derivative of the problem and plug in 2 for t

No derivatives needed, since you want the average velocity. (Use the formula you quoted.)

C: Dont really know . . .

Here's where you need a derivative.

 

[Moetasim]

I would like to clarify that the units for position are meters (m) and for time are seconds (s). With that in mind, the object's position at t=2s can be calculated by plugging in 2 for t in the given equation, resulting in r=24i+20jm.

To calculate the average velocity in the interval from t=0 to t=2s, we can use the formula V=change in r/change in t. The change in r would be the final position (r=24i+20jm) minus the initial position (r=0i+0jm), which gives us 24i+20jm. The change in t would be 2s-0s, which equals 2s. Therefore, the average velocity would be (24i+20jm)/2s = 12i+10jm/s.

To find the instantaneous velocity at t=2s, we can take the derivative of the position equation with respect to t, which would give us the velocity equation v=12i+(15-10t)j. Plugging in 2 for t would result in v=12i-5j. This means that at t=2s, the instantaneous velocity is 12i-5j m/s.