QUESTION

CSAT

Hard

Maths

Prelims 2018

The figure drawn below gives the velocity graphs of two vehicles A and B. The straight line OKP represents the velocity of vehicle A at any instant, whereas the horizontal straight line CKD represents the velocity of vehicle B at any instant. In the figure, D is the point where the perpendicular from P meets the horizontal line CKD such that PD=12LDPD= \frac{1}{2}LD.

5

What is the ratio between the distances covered by vehicles A and B in the time interval OL?

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Explanation

For Vehicle A (Triangle Area): Formula for distance covered by A: =0.5×OL×OP = 0.5 \times OL \times OP

Where: OL is the time interval, OP is the velocity of vehicle A at time L. For Vehicle B (Rectangle Area): Formula for distance covered by B: =OL×CK = OL \times CK

Where: OL is the time interval, CK is the constant velocity of vehicle B. Distance Ratio Formula: Formula for distance ratio (A:B): =(0.5×OL×OP)/(OL×CK) = (0.5 \times OL \times OP) / (OL \times CK) This gives the ratio of the distances, which simplifies to: =0.5×OP/CK = 0.5 \times OP / CK

Example Calculation: If we assume: OP=33 (velocity of vehicle A), CK=44 (velocity of vehicle B), OL=1010 (time interval), The result will be 0.5×3/4=0.3750.5 \times 3 / 4 = 0.375, or the ratio of the distances is 3:4.

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