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he distance. S metres, in which a car can stop is related to its speed, 'km/h by
S=pV+ qv² where p and q are constants. A car travelling at 10 km/h can stop in a distance of 5 metres
and at 20 km/h in a distance of 12 metres. Calculate the distance in which a car travelling at 30 km/h can stop
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As you read the problem, write two equations
10*p + 10^2*q = 5 meters (for the speed V = 10 km/h)
20*p + 20^2*q = 12 meters (for the speed V = 20 km/h)
Or, the same
10p + 100q = 5 (1)
20p + 400q = 12 (2)
To solve these equations, multiply equation (1) by 2 (both sides). Keep equation (2) as is
20p + 200q = 10 (1')
20p + 400q = 12 (2')
From equation (2'), subtract equation (1'). You will get
200q = 2
q = 2/200 = 0.01.
Then from equation (1)
10p + 100*0.01 = 5
10p = 5 - 1 = 4
p = 4/10 = 0.4.
Thus, now you know p= 0.4, q= 0.01.
Hence, at V= 30 km/h, the distance to stop is
30p + 30^2*q = 30*0.4 + 900*0.01 = 21,
ANSWER. The distance to stop at V 30 km/h is 21 meter.
Solved.