1. The position of a particle moving in a straight line during a5–second trip is s(t) =2t2 ? 2t + 2 cm.Find a time t at which the instantaneous velocity is equalto the average velocity for the entire trip beginning att = 0.
2. a) A particle moving along a line has positions(t) =t4 ? 34t2m at time t seconds. At which non negative times does theparticle pass through the origin? (Enter your answers as acomma-separated list. Round your answers to two decimalplaces.)
b) At which nonnegative times is the particle instantaneouslymotionless (that is, it has zero velocity)? (Enter your answers asa comma-separated list. Round your answers to two decimalplaces.)
3. The tangent lines to the graph off(x) =7x2 grow steeper asx increases. At what rate do the slopes of thetangent lines increase?
