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I don't understand what the graph is suppose to show and what the integral equation is suppose to mean. How would I use the graph to answer the questions?

f is the differentiable function whose graph is shown in the figure. The position at time t (sec) of a particle moving along a coordinate axis is meters. Use the graph to answer the questions. Give reasons for your answers.

s = S<-sigma 0 to t f(x)dx

graph: (1,1) (2,2) (3,3) continues to increase up to about (4,4) and decreases to (5,2) then decreases to about (7,-2) and increases to (9,0)

What is the particle's velocity at time t=5?
Is the acceleration of the particle at time t=5 positve or negative?
What is the particle's position at time t=3?
At what time during the first 9 sec does s have its largest value?

velocity is d s/dt, so s is the INT of velocity*time. You must be looking at a velocity vs time graph. The area under the graph is position. Area under the graph is the integral of v*dt.

The velocity at time 5 is read on the graph. Acceleration will be the derivative of veloicty, or the slope of the velocty plot.
Position at any time is the area under the curve from t=0 to time=t.

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