a. Suppose that the velocity of a body moving along the s-axis is

i) Find the body’s displacement over the time interval from t = 1 to t = 3 given that s = 5 when t = 0.

ii) Find the body’s displacement from t = 1 to t = 3 given that s = -2 when t = 0.

iii) Now find the body’s displacement from t = 1 to t = 3 given that s = s₀ when t = 0.

b. Suppose that the position s of a body moving along a coordinate line is a differentiable function of time t. Is it true that once you know an antiderivative of the velocity function ds/dt you can find the body’s displacement from t = a to t = b even if you do not know the body’s exact position at either of those times? Give reasons for your answer.

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ds dt = v= 9.8t - 3.