Multiple choice

A car is moving with at a constant speed of 60 km ${ h }^{ -1 }$ on a straight road. Looking at the rear view mirror, the driver finds that the car following him is at a distance of 100 m and is approaching with a speed of 5 km ${ h }^{ -1 }$. In order to keep track of the car in the rear, the driver begins to glance alternatively at the rear and side mirror of his car after every 2 s till the other car overtakes. If the two cars were maintaining their speeds, which of the following statement (s) is/are correct?

  1. The speed of the car in the rear is 65 km ${ h }^{ -1 }$
  2. In the side mirror, the car in the rear would appear to approach with a speed of 5 km ${ h }^{ -1 }$ to the driver of the leading car

  3. In the rear view mirror, the speed of the approaching car would appear to decrease as the distance between the cars decrease

  4. In the side mirror, the speed of the approaching car would appear to increase as the distance between the car decrease
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

The driver looks into the rear view mirror, which is a convex mirror, to keep track of the trailing car. In a convex mirror, the image velocity changes proportionally with the square of the magnification (m squared), and since magnification increases as the object approaches, the rate of change of image distance appears to decrease as the distance between the cars decreases.

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