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Matter In Our Surroundings

Question
CBSEENSC9005777

Both figures are shows the speed-time graphs of two cars (a) and (b) respectively.

Using these graphs answer the following questions:

(i) What is the acceleration of the car (a) and car (b) in the first two hours, in the next two hours and in the last two hours?

(ii) What is the total distance travelled by the two cars?

(iii) What is the average speed of the two cars? 



Fig. 8.29

Solution

i) Acceleration of car (a) in first two hours is given by, 
fraction numerator Change space in space speed over denominator time space taken end fraction space equals space fraction numerator 30 minus 0 over denominator 2 minus 0 end fraction equals 30 over 2 space equals space 15 space km divided by straight h squared
Acceleration of car (A) in the next two hours is given by, 
fraction numerator 60 minus 30 over denominator 4 minus 2 end fraction space equals space fraction numerator 30 space k m divided by h r over denominator 2 space h end fraction space equals space 15 space km divided by straight h squared
Acceleration of car (a) in the last two hours, 
fraction numerator 0 minus 30 over denominator 8 minus 6 end fraction space equals space fraction numerator negative 30 space k m divided by h r over denominator 2 space h end fraction equals negative space 15 space k m divided by h squared
The negative accelerations means that the car is deccelerating. 
ii) Total distance travelled by the car (a) in 8 hours is, 
Area of increment ABC =  1 half cross times b a s e cross times h e i g h t
1 half cross times left parenthesis 8 minus 0 right parenthesis space cross times space left parenthesis 60 minus 0 right parenthesis space equals space 240 space k m 
iii) Average speed of the car (a) is,  
equals space fraction numerator Total space distance space travelled over denominator Time space taken end fraction
equals 240 over 8
equals space 30 space km divided by hr