AP Calc- Unit 1 Review

An object dropped from a state of rest at time t=0 travels a distance s(t)=4.9t^2 meters in t seconds.
How far does the object travel during the time interval [2.5, 3]? Round to the nearest thousandth.
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Suppose Neil Armstrong decided to throw a golf ball into the air while he was standing on the moon and that the height of the golf ball was modeled by the equation below, where s is measured in feet and t is measured in seconds. s(t)=-2.72t^2+26.9t+6. Find the best approximation for the instantaneous rate of change (velocity) of the golf ball at 7 seconds using 7.0001 seconds. Round to the nearest thousandth.
A pendulum swings from the ceiling. Its distance, d, in feet, from one wall of the room depends on the number of seconds, t, since it was set in motion. Assume that the equation from d as a function of t is d(t)=20+16cos((pi/3)t). You want to find out how fast the pendulum is moving at a given instant, t, and whether it is approaching or going away from the wall.
Find d when t=4.
A pendulum swings from the ceiling. Its distance, d, in feet, from one wall of the room depends on the number of seconds, t, since it was set in motion. Assume that the equation from d as a function of t is d(t)=20+16cos((pi/3)t). You want to find out how fast the pendulum is moving at a given instant, t, and whether it is approaching or going away from the wall.

Estimate the instantaneous rate of change of d with respect to t when t=2.5 using 2.5001 seconds. Round to the nearest thousandth.

At that time, is the pendulum approaching the wall or moving away from it? Why? What is the distance doing?
what is average velocity?Δposition/Δtime Δd/ΔtWhat is the definition of average velocity?the ratio of the change in position to the elapsed time periodWhat is the definition of instantaneous velocity?indicates the speed and direction of some object at a particular moment, which could be faster or slower than the average velocityWhat is the definition of AROC or Average speed?the total distance traveled, d, divided by the elapsed time period, tGraphically, the average speed is the slope of the secant lineAnalytically, average speed (AROC)=Δd/ΔtWhat is the definition of Instantaneous Speed? (IROC)the speed at a specific instant in time, where t=t0 is the limit of the average rate of changeGraphically, the instantaneous speed is the slope of the tangent line at a specific pointAnalytically, we need calculus to determine this instantaneous speedLimits are what?A statement that tells you what height a function INTENDS to reach as you get close to a specific x-valueright hand limitx->c^+left hand limitx->c-general limitx->c