Acceleration from velocity-time graph
By a process of reasoning similar to that used in the section above relating to the distance-time graphs, it may be shown that,
A stone is thrown vertically upwards with an initial velocity of 14 m/s. Neglecting air resistance, find: (a) the maximum height reached; (b) the time taken before it reaches the ground. (Acceleration due to gravity = 9.8 m/s”) When working problems of this type the reader is recommended to extract the data given in the question and write them down against the appropriate symbols before attempting to substitute in one of the equations of motion.
A car starts from rest and is accelerated uniformly at the rate of 2 m/s2 for 6 s. It then maintains a constant speed for half a minute. The brakes are then applied and the vehicle uniformly retarded to rest in 5 s. Find the maximum speed reached in km/h and the total distance covered in metres. First stage u = 0 m/s a = 2 m/s2 Substituting in the first equation of motion,
The distance moved in the first stage may be found by substituting in the second
equation of motion, thus,
Alternative graphical solution
Fig. 3.5 shows the velocity-time graph for the previous problem, in which OA, AB and BC represent the three stages of the motion respectively. The distance moved is numerically equal to the area of the figure OABC (a trapezium).