Question

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

• A. 70.7 km/hr along south-west direction
• B. zero
• C. 50 km/hr along west
• D. 70.7 km/hr along north-west direction

Answer 1

Answer: (A)

$v_1=50km/hr$ due north
$v_2=50km/hr$ due west
$-v_1=50km/hr$ 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