1. The problem statement, all variables and given/known data The position of a ball moving on a straight line has an equation of p(t) = 1/3t^3 - 2t^2 +3t , where p is its position and s is time in seconds 1. At what times is the ball at rest? 2. Using its velocity and acceleration, determine the balls DIRECTION and if it is SPEEDING UP or SLOWING DOWN at 2.5 seconds 3. Find the TOTAL DISTANCE the ball travels in the first 6 seconds. 3. The attempt at a solution For 1, it is simple quadratics which I found the ball at rest to be at 0 seconds and also at 3 seconds For 2, I believe that the first derivate equals velocity and the second derivative equals acceleration. p'(t) = t^2 - 4t + 3 p"(t) = 2t - 4 For 2, would I be subbing in the time of 2.5s into my equation? If I do, I get a negative value which means that the velocity would be decreasing, correct? However, for the acceleration, I get a positive 1. Could someone please explain what that means? Would the ball also be moving in the straight linear direction still? 3. For this, I just subbed in 2.5 into first derivate which gave me 15m/s, I than multiplied by the 6 seconds and got 90 meters. Is this correct? Or Should i be subbing the 6 seconds into my original equation?