On an essentially frictionless, horizontal ice rink, a skater mowing at 3.0 m/s encounters a rough patch that reduces her speed to 1.65 m/s due to a friction force that is 25% of her weight. Use the work—energy theorem to find the length of this rough patch.

If a rock is thrown upward on the planet mars with a velocity of 10 mys, its height in meters t seconds later is given by y − 10t 2 1.86t 2 . (a) find the average velocity over the given time intervals: (i) [1, 2] (ii) [1, 1.5] (iii) [1, 1.1] (iv) [1, 1.01] (v) [1, 1.001] (b) estimate the instantaneous velocity when t − 1.