EXAMPLE 3 Given x as a function of t. A jet engine moves along an exper- imental track (which we call the x axis) as shown in Fig. 13a . We will treat the engine as if it were a particle. Its position as a function of time is given by the equation x=At^2+B where A=2.10m/s^2 and B=2.80m , and this equa- tion is plotted in Fig. 13b. (a)Determine the displacement of the engine during the time interval from t_(1)=3.00 s to t_(2)=5.00s (b) Determine the average velocity during this time interval. (c)Determine the magnitude of the instanta- neous velocity at t=5.00s

Question

Answer 1

(a) To determine the displacement of the engine during the time interval from

s to

, we need to find the difference in position at these two times. We can do this by plugging in the values of

and

into the equation

and subtracting the two results.Using

s:

mUsing

s:

mThe displacement is then:

m(b) To determine the average velocity during this time interval, we can use the formula:

where

sPlugging in the values:

m/s(c) To determine the magnitude of the instantaneous velocity at

s, we need to find the derivative of the position function

with respect to time

and evaluate it at

s.The derivative of

with respect to

is:

Plugging in

s:

m/sTherefore, the magnitude of the instantaneous velocity at

s is

m/s.

Soru