A sprinter of 100 m race, covers 4 m in first second, 30 m in next 4 seconds and 52m in amother 4 seconds and finishes the race in 10 seconds. (i)Calculate the average speed of the sprinter ? (ii) what is the peak value  attained by the sprinter ? (iii) during which time interval is the acceleration is the highest ? (iv) Plot the distance time graph and velocity time graph for the race ? (iv) show on the graph the velocity of the sprinter at the end of 5 seconds ?

Asked by Vikas | 6th Jul, 2017, 12:32: PM

Expert Answer:

begin mathsize 12px style left parenthesis straight i right parenthesis space Average space velocity space equals space fraction numerator Total space distance space travelled space over denominator Total space time space taken end fraction space
rightwards arrow space Average space velocity space equals space fraction numerator 100 space straight m over denominator 10 space straight s end fraction space equals space 10 space straight m divided by straight s space end style
 
(ii)  For all the time intervals we need to calculate the initial velocity, acceleration, displacement and the final velocity
Formulas used:
s = ut + (1/2)at2 and v = u + at
 
Time s 0 1 5 9 10
Distance m 0 4 34 86 100
Velocity m/s 0 8 7 19 9
 
So, peak velocity attained by the is 19 m/s at the end of the 9th second.
 
(iii) Acceleration is highest between 5th to 9th second. It is 3 m/s2.
 
(iv) 
(v)
Mark the points from 5 second on the graph and note down the corresponding reading on the velocity scale.
Then, calculate the slope.

Answered by Yashvanti Jain | 6th Jul, 2017, 06:48: PM