The accompanying figure shows the position versus time curve for an automobile over a period of time of 5 s. Use the line segments shown in the figure to estimate the instantaneous velocity of the automobile at time t = 2 s and again at time t = 4 s. Round your answers to two decimal places, if required. Instantaneous velocity at t = 2 s = m/s Instantaneous velocity at t = 4 s = m/s
![The velocity-time graph of a car moving along a straight road is shown in Figure 3 below. [Assumption: The car is travelling in a straight line. ] Figure 3 (Not drawn to scale) a) Determine the velocity of the car at time t = 1 s. b) Determine the acceleration of the car at time t = 5 s. c) Determine the rate of change of velocity of the car at time t = 7 s. d) Determine the displacement of the car from time t = 4 s to t = 6 s. e) Determine the average velocity of the car from time t = 0 s to t = hs, leave your answer in terms of h. f) When the car starts moving from rest at time t = 0 s, a lorry travelling with a uniform constant velocity of vm/s passes by the car. At t = 4 s, the car and lorry have the same displacement. Determine the value of v. g) When the car starts moving from rest at time t = 0 s, a motorcycle travelling with a uniform constant velocity of 16 m/s passes by the car. The motorcycle maintains this uniform velocity for 2 s before decelerating uniformly to rest at t = 10 s. The car overtakes the motorcycle at time t = ws, where 4 < w < 6. Determine the value of w.](https://www.doubtrix.com/uploads/editor/7775664077JfqMMcGvFj.png)
![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)