The position of a particle in meters is given by x =2.5t + 3.1t ^2 - 4.5t^3, where t is the time in seconds. What are the instantaneous velocity and instantaneous acceleration at t = 0.0 s? At t = 2.0 s? What are the average velocity and average acceleration for the time interval 0 greater than or equal to t less than or equal to 2.0 s?

The acceleration of a bus is given by ax(t) = αt, where α = 1.15 m/s3 is a constant. a. If the bus's velocity at time t1 = 1.05 s is 4.90 m/s, what is its velocity at time t2 = 2.20 s? b. If the bus's position at time t1 = 1.05 s is 6.05 m, what is its position at time t2 = 2.20 s?

The velocity of a particle at any time t moving along an x-axis is given by the following equation: v = 3t^2 - 8t + 3 where v is in m/s. At t = 0, x = 0. Determine the following:(a) the particle's displacement between t = 0 and t = 4 s (b) the average velocity for the time interval t =0 to t = 4 s (c) the acceleration when t =3 s (d) the instantaneous velovity at t = 4 s (e) what is the initial direction of motion of the particle?

From t = 0 to t = 4.14 min, a man stands still, and from t = 4.14 min to t = 8.28 min, he walks briskly in a straight line at a constant speed of 1.60 m/s. What are (a) his average velocity vavg and (b) his average acceleration aavg in the time interval 1.00 min to 5.14 min? What are (c) vavg and (d) aavg in the time interval 2.00 min to 6.14 min?

The position of a particle moving along the x axis is given by x=3t2-15t-10m, where t is in s, Determine the following a. average velocity during the time interval t=2.5 s to t=4.5s b. instantaneous velocity at 3s c. average acceleration during the time interval t=2.5 s to t=4.5s d. instantaneous acceleration at 3s e. is the particle speeding up or slowing down at 4s? justify your answer

The engine of a model rocket accelerates the rocket vertically upward for 2.0 s as follows: At t = 0, the rocket's speed is zero; at t = 1.0 s, its speed is 5.0 m/s; and at t = 2.0 s, its speed is 22 m/s. Plot a velocity vs. time graph for this motion, and use the graph to determine each of the following. (a) the rocket's average acceleration during the 2.0 s interval                m/s2 (b) the instantaneous acceleration of the rocket at t = 1.5 s                   m/s2

Suppose an object starts at time t=0s at a position defined as x=0m. At t=0.5s, the object is at x=1.5m, and at t=1.0s, the object is at x=2.0m. What is the average velocity for the first interval (approximated at t=0.25s) and for the second interval (approximated at t=0.75s)? In the example above, what is the average acceleration of the object?

The position of a rabbit along a straight tunnel as a function of time is plotted in the figure. What is its instantaneous velocity at t=10.0s? What is its instantaneous velocity at t=30.0s? What is its average velocity between t=0 and t=5.0s? What is its average velocity between t=25.0s and t=30.0s? What is its average velocity between t=40.0s and t=50.0s?

a particle moves in one dimension, and its position as a function of time is given by x = (1.9m/s)t + (-2.6 m/s^2)t^2  what is the particles average velocity from t = 0.45 s to t = 0.55 s?    what is the particles average velocity from t = 0.49 s to t = 0.51 s?

A ball is projected upward at time t = 0.0 s, from a point on a roof 90 m above the ground. The ball rises, then falls and strikes the ground. The initial velocity of the ball is 61.2 m/s. Consider all quantities as positive in the upward direction. At time tt = 1.6 s, the acceleration of the ball is closest to: A.-10 m/s B. -5 m/s C. +10 m/s D. zero E. +5 m/s^2