The aim is to get a high acceleration so as to reach max velocity quickly, to have a high max velocity and to maintain that for as much of the race as possible. Finally, he looks to have a gradual deceleration.
During the max velocity stage of the race he tries to increase his stride length (s) and frequency (i.e. reduce the time (t) for each stride). He uses various techniques and training methods,but in essence, it is these two simple factors that a sprinter works on.
SAMPLE PROBLEM 2K
A gazelle accelerates from rest up to a velocity of 20 m s1 in 4 s in order to escape a lioness.The gazelle runs at this velocity for a further 10 s before being caught by the lioness. Sketch a velocity−time graph of this motion. Use the graph to calculate:
(i) the gazelle’s acceleration (ii) the distance travelled before the lioness caught the gazelle
SAMPLE ANSWER 2K (i) acceleration slope
slope
y2 y1 x2 x1
Qa 20 0 4 5
The acceleration of the gazelle was 5 m s2.
(ii)
20 0 4 14 Time / s
Fig 2.21: Sketch of the velocity–time graph of the gazelle’s motion
distance area
1 2 (base)(height) (base)(height)
1 2 (4)(20) (10)(20) 240
The distance travelled by the gazelle was 240 m. 240
EXERCISE 2.4 DISTANCE–TIME AND VELOCITY–TIME GRAPHS
Q1 A boy travels at constant velocity, covering a distance of 15 m in 5 s. He remains at that point for a further 6 s before returning at constant velocity in 10 s. Draw a distance–time graph of the boy’s motion and use it to calculate his velocity on the outward journey.
Q2 An object starts from rest and accelerates at 2 m s2. By calculating the distance travelled after each second, sketch the distance–time graph for the first 3 s of its motion.
Q3 A speedboat starts from rest and reaches a velocity of 20 m s1 in 10 s. It continues at this velocity for a further 5 s.The speedboat then comes to a stop in the next 4 s. (i) Draw a velocity–time graph to show the variation of velocity of the boat during its journey. (ii) Use your graph to estimate the velocity of the speedboat after 6 s. (iii) Calculate the acceleration of the boat during the first 10 s. (iv) What was the distance travelled by the boat when it was moving at a constant velocity?
