velocity problem

[susumandrai]

The displacement s(t) of a remote controlled car from its operator who is stationary in metres is given by the formula s(t) = (1/3)t^3 -t^2 - 8t + 8, where t is the time in seconds. The graph of s(t) is shown here:

a. Find the average velocity (rate of change of displacement) of the car between t=2 and t=4. b. Find the instantaneous velocity of the car after 4 seconds. I really dont know what the above two questions mean. Please help

 

[galactus]

The displacement s(t) of a remote controlled car from its operator who is stationary in metres is given by the formula s(t) = (1/3)t^3 -t^2 - 8t + 8, where t is the time in seconds. The graph of s(t) is shown here:

View attachment 1933

Velocity is the derivative of the position function, s(t). You are given the position function. Acceleration is the second derivative of s(t).

a. Find the average velocity (rate of change of displacement) of the car between t=2 and t=4. The average velocity is found by \(\displaystyle \frac{f(t_{1})-f(t_{0})}{t_{1}-t_{0}}\) In other words, sub t=4 into your given function. Sub t=2 into your given function. Subtract them and divide by 2. b. Find the instantaneous velocity of the car after 4 seconds. Take the derivative of your function and sub in t=4.

 

[HallsofIvy]

For (b), the "derivative" is also the slope of the tangent line. In this particular problem, it is very easy to see that the tangent line to the graph is horizontal at t= 4 and so its slope is 0.