In: Math
1. The position of a particle moving in a straight line during a 5–second trip is s(t) = 2t2 − 2t + 2 cm. Find a time t at which the instantaneous velocity is equal to the average velocity for the entire trip beginning at t = 0.
2. a) A particle moving along a line has position s(t) = t4 − 34t2 m at time t seconds. At which non negative times does the particle pass through the origin? (Enter your answers as a comma-separated list. Round your answers to two decimal places.)
b) At which nonnegative times is the particle instantaneously motionless (that is, it has zero velocity)? (Enter your answers as a comma-separated list. Round your answers to two decimal places.)
3. The tangent lines to the graph of f(x) = 7x2 grow steeper as x increases. At what rate do the slopes of the tangent lines increase?