A particle moving along a line has a displacement according to the function x(t)=t2−2t+4,𝑥(𝑡)=𝑡2−2𝑡+4, where x is measured in meters and t is measured in seconds. Find the average velocity over the time period t=[0,2].

The position of an object moving along x-axis is given by x = a + bt2 where a = 8.5 m, b =2.5 m s–2 and t is measured in seconds. What is its velocity at t = 0 s and t = 2.0 s. Whatis the average velocity between t = 2.0 s and t = 4.0 s ?

A particle moves along a line with a velocity v(t)=t2+3t−4, measured in meters per second. Find the total distance the particle travels from t=0 seconds to t=2 seconds.Enter an exact answer.Provide your answer below:

The position of a particle moving in a straight line is given by the function S (t) = t3 − 6t2,t ≥ 0. The graph of S against t is shown. The corresponding velocity–time graph is alsoshown. The function describing the velocity is V(t) = 3t2 − 12t.1 2 3 41 2 3 45 650–5–10–10–20010–30S(t) = t3 – 6t2 V(t) = 3t2 – 12tVSt ta Find the average velocity of the particle for the intervals:i [3.5, 4.5] ii [3.9, 4.1] iii [3.99, 4.01]b From part a, what is the instantaneous velocity when t = 4?c i For what values of t is the velocity positive?ii For what values of t is the velocity negative

The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.a(t) = 2t + 2,    v(0) = −15,    0 ≤ t ≤ 5(a) Find the velocity at time t.v(t) = m/s(b) Find the distance traveled during the given time interval.

A particle's (x, t) coordinates at two instants are A (x=-14m, t=3s) and B (x=6m, t=1s). What is the particle's average velocity during this time?