The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 2 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places. ) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s
![The displacement (in centimeters) of a particle s moving back and forth along a straight line is given by the equation s = 2 sin(πt) + 4 cos(πt), where t is measured in seconds. (Round your answers to two decimal places. ) (a) Find the average velocity during each time period. (i) [1, 2] cm/s (ii) [1, 1.1] cm/s (iii) [1, 1.01] cm/s (iv) [1, 1.001] cm/s (b) Estimate the instantaneous velocity of the particle when t = 1. cm/s](https://www.doubtrix.com/uploads/editor/9947714394TPgahcSJtp.png)
![If an arrow is shot upward on Mars with a speed of 54 m/s, its height in meters t seconds later is given by y = 54t − 1.86t2. (Round your answers to two decimal places.) (a) Find the average speed over the given time intervals. (i) [1, 2] m/s (ii) [1, 1.5] m/s (iii) [1, 1.1] m/s (iv) [1, 1.01] m/s (v) [1, 1.001] m/s (b) Estimate the speed when t = 1. m/s](https://www.doubtrix.com/uploads/editor/3138862167HSNDiccNXu.png)
![The normal monthly precipitation at the Seattle-Tacoma airport can be approximated by the model shown below, where R is measured in inches and t is the time in months, with t = 0 corresponding to January 1. (Round your answers to two decimal places.) R = 2.876 + 2.202 sin(0.576t + 0.847) (a) Determine the extrema of the function over a one-year period. relative minimum (t, R) = ( ), relative maximum (t, R) = ( ), (b) Use integration to approximate the normal annual precipitation. (Hint: Integrate over the interval [0, 12].) in (c) Approximate the average monthly precipitation during the months of June, July, and August. in](https://www.doubtrix.com/uploads/editor/2944063509AgmljYiKFe.png)
![(a) A particle which is moving in a straight line with constant acceleration 2 m/s2 is initially at rest. Find the distance covered by the particle in the third second of its motion. [4 marks] (b) The time variation of the position of a particle in rectilinear motion is given by x = 2t3 + t2 + 2t. If v is the velocity and a is the acceleration of the particle. Find the velocity and acceleration of the particle when t = 3 s. [4 marks] (c) A bicycle moves along a straight road such that its position is described by the graph shown. Construct the v−t graph and a−t graph for 0 ≤ t ≤ 30 s.](https://www.doubtrix.com/uploads/editor/7222719326dsBBXaPfWp.jpg)