Q. A bus is moving on a straight road towards north with a uniform speed of $50$ km/hour then it turns left through $90^{\circ}$. If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is
AIPMTAIPMT 1989Motion in a Plane
Solution:
$v_{1}=50 \,km / hr$ due north
$v_{2}=50\, km / hr$ due west
$-v_{1}=50 \,km / hr$ due south
Magnitude of change in velocity
$=\left|\vec{v}_{2}-\vec{v}_{1}\right|=\left|\vec{v}_{2}+\left(-\vec{v}_{1}\right)\right|$
$=\sqrt{v_{2}^{2}+\left(-v_{1}\right)^{2}}$
$=\sqrt{(50)^{2}+(50)^{2}}$
$= 70.7$ km/hr along south-west direction
