Explanations & Calculations
- When it is needed to check the rate of change of some variable it is necessary to check for the derivative of that with respect to time.
- like, the rate of change of displacement is called the velocity & the rate of change of velocity is called the acceleration.
- To derive a convenient equation, consider the figure below.
- Neglect the height of the radar station & consider the 1km is measured from there.
- Consider a moment after passing the at a time of t, then the distance covered is vt .
- Then r can be written as,
cos(120)2vtcos(120)2vcos(120)×1dtdrdtdrt=601h=2(vt)(1km)(vt)2+(1km)2−r2⋯(1)=v2t2−r2−1=2v2t−2rdtdr−0=2r2v2t−2vcos(120)=2r2(300kmh−1)2(601h)−2(300)(−0.5)=r1650
- To calculate r at one minute time, the same (1) equation can be used.
−0.5r=2(300×601)(1)(300×601)2+1−r2=5.568km
dtdrt=601=5.568km1650km2h−1=296.336kmh−1
- Note that the time— one minute— was expressed in hours, due to the speed being in the units of kmh−1
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