An object moves along the x axis according to the equation x = 3.00t2 2.00t + 3.00, where x is in meters and t is in seconds. Determine (a) the average speed between t = 2.00 s and t = 3.00 s, (b) the instantaneous speed at t = 2.00 s and at t = 3.00 s, (c) the average acceleration between t = 2.00 s and t = 3.00 s, and (d) the instantaneous acceleration at t = 2.00 s and t = 3.00 s. (e) At what time is the object at rest?

A particle moves along the x axis according to the equation x = 2.00 + 3.00t 1.00t2, where x is in meters and t is in seconds. At t = 3.00 s, find (a) the position of the particle, (b) its velocity, and (c) its acceleration.

At an air show, a jet plane has velocity components vx= 695km/h and v  y =415km/h at time 4.35 s and v x =938km/h and V y =365km/h at time 7.52s. A)For this time interval, find the xxx component of the plane's average acceleration. b)For this time interval, find the yyy component of the plane's average acceleration. C)For this time interval, find the magnitude of its average acceleration. D)For this time interval, find the direction of its average acceleration.

The figure below is the position vs time graph for a moving object. What is the object's average velocity (a) between t=0s and t=1.0s? (b) between t=Os and t=4.0s? (c) between t=3.0s and t=6.0s? (d) What is its average speed for each of the time segments in parts a/b/c? In your solution write-up, be sure to clearly define and label variables, begin all calculations by expanding an equation definition using the variables needed for that particular part (that is, one should be able to tell which part the solution belongs to even if 'part a', 'part b' etc were omitted), and show all steps for your calculations. x (m) 4 3 1 t (s) 6. 1 3 4 5 2.

In heavy rush-hour traffic, you drive in a straight line at 12 m/s for 1.5 minutes, then you have to stop for 3.5 minutes, and finally, you drive at 15 m/s for another 2.5 minutes. Plot a position-versus-time graph for this motion. Your plot should extend from t = 0 minutes to t = 7.5 minutes. Assume x=0 and t=0 at the start of your motion.

A thief is trying to escape from a parking garage after completing a robbery, and the thief’s car is speeding (v = 11 m/s) toward the door of the parking garage (Fig. P2.60). When the thief is L = 14 m from the door a police officer flips a switch to close the garage door. The door starts at a height of 7 m and moves downward at 0.3 m/s. If the thief’s car is 1.4 m tall, will the thief escape? (Find the height of the door above the ground).

An object accelerating at constant acceleration (a) has an initial velocity v0 (at t=0), a velocity v at time t, and goes a particular distance d or x - x0 during the time interval.  Derive the expression relating v0, v, a, and d (or x-x0).  The relation must not include time.  You may use either algebra or calculus.

A bus makes a trip according to the position-time graph shown in the drawing. What is the average velocity (magnitude and direction) of the bus during (a) segment A, (b) segment B, and (c) segment C? Express your answers in km/h.

A particle moves along the x axis beginning at x = −2 m at time zero. The particle moves forward at speed 4 m/s for 3 seconds, then backward at 3 m/s for 2 seconds, then forward again at 1 m/s for 3 seconds. Draw a position vs. time graph for this motion. Draw a velocity vs. time graph for the same motion.