Suppose that a ball is dropped from the upper observation deck of the CN Tower in Toronto, 450 m above the ground. Find the velocity of the ball after 3 seconds.SolutionThe difficulty in finding the velocity after 3 seconds is that we are dealing with a single instant of time (t = 3), so no time interval is involved. However, we can approximate the desired quantity by computing the average velocity over the brief time interval of a tenth of a second from t = 3 to t = 3.1.average velocity  =  change in positiontime elapsed =  s(3.1) − s(3)0.1 =  4.9 2  − 4.9 2 0.1 =  m/s.The following table shows the results of similar calculations of the average velocity over successively smaller time periods.Timeinterval Averagevelocity (m/s)3 ≤ t ≤ 434.33 ≤ t ≤ 3.129.893 ≤ t ≤ 3.0529.6453 ≤ t ≤ 3.0129.4493 ≤ t ≤ 3.00129.4049It appears that as we shorten the time period, the average velocity is becoming closer to m/s (rounded to one decimal place). The instantaneous velocity when t = 3 is defined to be the limiting value of these average velocities over shorter and shorter time periods that start at t = 3. Thus the (instantaneous) velocity after 3 s is the following. (Round your answer to one decimal place.)v = m/s

If a ball is thrown in the air with a velocity 50 ft/s, its height in feet t seconds later is given by y = 50t − 16t2.(a) Find the average velocity for the time period beginning when t = 2 and lasting(i)    0.5 second. ft/s(ii)    0.1 second. ft/s(iii)    0.05 second. ft/s(iv)    0.01 second. ft/s(b) Estimate the instantaneous velocity when t = 2. ft/s

A ball is thrown vertically upward froma height of 40 m and hits the groundwith a speed that is three times itsinitial speed. What is the time taken (insec) for the fall (Take 𝑔 = 10 𝑚/𝑠2)

The path of a baseball relative to the ground can be modelled by the function 𝑑(𝑡)=−𝑡2+8𝑡+1 where 𝑑(𝑡) represents the height of the ball in metres after 𝑡 seconds.Find the average rate of change of the ball between 1 and 3 seconds. Bold text start[4 marks]Bold text EndUsing the secant method, find the instantaneous rate of change at 2 seconds.

Jen served the final point before winning her tennis match! She tossed the ball up into the air from a height of 5 feet with a velocity of 22 feet per second. After the ball started to come back down, Jen hit the ball with her racket at a height of 6 feet.Which equation can you use to find how many seconds the ball was in the air before Jen hit it?If an object travels upward at a velocity of v feet per second from s feet above the ground, the object's height in feet, h, after t seconds can be modeled by the formula h=–16t2+vt+s.6=–16t2+22t+55=–16t2+22t+6To the nearest tenth of a second, how long was the ball in the air before Jen hit it? seconds

A stone is released from the top of a tower of height 980 m. Calculate its velocity after 3 seconds. (Take g = 9.8 m/s2)