(5) The displacement (in metres) of a particle at time t seconds is given by s = 4000t² - 10t¹ for 0 ≤ t ≤ 20. = d. (a) Find the velocity of the particle v = d's dt2. (b) Find the acceleration of the particle a = (c) What is the displacement, velocity and acceleration at time t = 10 seconds?

2. The distance traveled (in feet) by a car t seconds after acceleration from rest is given by s(t) = 8t2 a) Find the average velocity of the car over the given time intervals. (Include units) i) [5,5.05] ii) [5,5.01] iii) [5, 5.001] b) Estimate the instantaneous velocity of the car after 5 seconds. (Include units)

Suppose an object moves along the y-axis so that its location is y = 2x² +8 at time x (where y is measured in meters and r is in seconds). (a) Find the average velocity of the object, for a changing from 1 to 5 seconds. (b) Find the instantaneous velocity of the object at 2 seconds. ation- t they >-vent ength ed. points w te with action is not merentiable. Give a brief reason why the points are not differentiable.

8) A runner was training for a 21 mile long race. The distance D (in miles) in function of time t (in weeks) is given by: D = 2(t-1)² +15 a) b) c) How many miles have done the runner in the first week? What is the average rate of training between the first and the third week? dD Calculate the derivative of D with respect to time dt and explain the obtained answer.

Find y''. X y = 4 cot (76) 10 O A. OB. 2 25 O C. - 8 csc O D. CSC 2 5 2 CSC 2 X 10 X 10 X 10 cot X 10 X X 2 8 csc ² [+] cot (16) 圖 10 10

True or false: If f(t) is the distance of a particle from a fixed point after tunits of time, then f' (t) is the instantaneous velocity of the particle after tunits of time.

A function f(x) satisfies f(-7.3) = 6.6 and f'(-7.3) = -8.8. What is the equation of the tangent line of f(x) at x = -7.3? a.y=--8.8x + -37.84 O b. y = -8.8x + -77.44 Oc. y = --8.8x + -97.24 Od. y = -8.8x + 84.04 Oe. y=--8.8x + 24.64 O f. y = -8.8x + -57.64

Given that the distance in feet that a car moves in t seconds is given by d(t) d'(15) = 900 X ft/sec = 4t². Find the instantaneous velocity in feet per second when t = 15, d'(15). (Enter an exact number.)

Find y' at the specified point. q² + y? = 81 , at (0, – 9) - y'