An object\'s position is given by x=bt+ct^3, where b=1.50m/s and c=0.640m/s^3. T
ID: 2226256 • Letter: A
Question
An object's position is given by x=bt+ct^3, where b=1.50m/s and c=0.640m/s^3. To study the limiting process leading to the instantaneous velocity, calculate the object's average velocity over time intervals from 1.00s to 3.00s. Then Calculate the object's average velocity over time intervals from 1.50s to 2.50s. Calculate the object's average velocity over time intervals from 1.95s to 2.05s Find the instantaneous velocity as a function of time by differentiating.Explanation / Answer
Definition Average Speed V=distance/time interval let at t1 point is at x1 so from the given eqn x1=bt1+ct1^3 similarly at point x2 x2=bt2+ct2^3 Displacement=x2-x1=b(t2-t1)+c(t2^3-t1^3) hence the average vel is V=x2-x1/(t2-t1)=b+c(t2^3-t1^3)/(t2-t1) for the Q.1 t2=3 t1=1 so t2-t1=2 t2^3-t1^3=27-1=26 ==> V=b+26/2.c=b+13c=1.5+13x0.649=9.94m/s use the same method for Q.2 and Q.3 also Now for Q.4 for instantaneous vel we get by differentiating dx/dt=b+3t^2