1. The position versus time for a certain particle moving along the x axis is shown in Figure P2.1. Find the average velocity in the time intervals
(a) 0 to 2s,
(b) 0 to 4s,
(c) 2s to 4s,
(d) 4s to 7s,
(e) 0 to 8s.
View Detail ... 2. A position–time graph for a particle moving along the x axis is shown in Figure P2.5.
(a) Find the average velocity in the time interval `t = 1.50 s` to `t = 4.00 s`.
(b) Determine the instantaneous velocity at `t = 2.00 s` by measuring the slope of the tangent line shown in the graph.
(c) At what value of `t` is the velocity zero?
View Detail ... 3. The position of a particle moving along the x axis varies in time according to the expression `x = 3t^2`, where `x` is in meters and `t` is in seconds. Evaluate its position
(a) at `t = 3.00 s` and
(b) at `3.00 s + ∆t`.
(c) Evaluate the limit of `∆x//∆t` as `∆t` approaches zero to find the velocity at `t = 3.00 s`.
View Detail ... 4. Find the instantaneous velocity of the particle described in Figure P2.1 at the following times:
(a) `t = 1.0 s`,
(b) `t = 3.0 s`,
(c) `t = 4.5 s`, and
(d) `t = 7.5 s`.
View Detail ... 5. A hare and a tortoise compete in a race over a straight course `1.00 km` long. The tortoise crawls at a speed of `0.200 m//s` toward the finish line. The hare runs at a speed of `8.00 m//s` toward the finish line for `0.800 km` and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at `8.00 m//s`. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds.
(a) How far is the tortoise from the finish line when the hare resumes the race?
(b) For how long in time was the hare stationary?
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