JEE Main Physics Class 11 Motion in a Straight Line and Plane Part 1 Questions

Let the car turn of the highway at a distance 'x' from the point M. So, RM = x
And if speed of car in field is v, then time taken by the car to cover the distance QR = QM – x on the highway,
t1=

QM−x

2v

....(i)
Time taken to travel the distance 'RP' in the field
t2=

√d2+x2

v

...(ii)
Total time elapsed to move the car from Q to P
t=t1+t2=

QM−x

2v

+

√d2+x2

v

For ′t′ to be minimum

dt

dx

=0

1

v

[−

1

2

+

x

√d2+x2

]=0
or x=

d

√22−1

=

d

√3