1- A car travels up a hill at a constant speed of 42 km/h and returns down the hill at a constant speed of 61 km/h. Calculate the average speed for the round trip.
2-The position function x(t) of a particle moving along an x axis is x = 5.00 - 7.00t2, with x in meters and t in seconds.
(a) At what time and
(b) where does the particle (momentarily) stop?
At what (c) negative time and (d) positive time does the particle pass through the origin?
3-The position of a particle moving along an x axis is given by x = 16.0t2 - 5.00t3, where x is in meters and t is in seconds.
Determine (a) the position,
(b) the velocity, and
(c) the acceleration of the particle at t = 7.00 s.
(d) What is the maximum positive coordinate reached by the particle and
(e) at what time is it reached?
(f) What is the maximum positive velocity reached by the particle and
(g) at what time is it reached?
(h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)?
(i)Determine the average velocity of the particle between t = 0 and t = 7.00 s.
4-The position of a particle moving along the x axis depends on the time according to the equation x = ct4 - bt5, where x is in meters and t in seconds. Let c and b have numerical values2.5 m/s4 and 1.4 m/s5, respectively. From t = 0.0 s to t = 2.1 s,
(a) what is the displacement of the particle?
Find its velocity at times (b) 1.0 s, (c) 2.0 s, (d) 3.0 s, and (e) 4.0 s. Find its acceleration at (f) 1.0 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s.