An automobile starts from rest at a traffic light, gains speed, cruises, and then brakes to a stop. The speedometer readings taken at several instants are:
Time t (s): \; 0 4 7 11 15
Velocity v (m\,s−1): \; 0 10 18 18 0
Assume the velocity changes uniformly between successive readings.
(i) Plot the velocity–time graph for the entire 15\,s motion on graph paper, taking suitable scales.
(ii) Using your graph, determine the magnitude and sign of acceleration during each of the four successive intervals.
(iii) Calculate the total displacement of the automobile in the 15\,s journey.
(iv) Find the average velocity and the average acceleration for the complete motion from t=0 to t=15\,s.