Let v be the minimum velocity of student so, that he could catch the bus
If student catch the bus in time t, then distance travelled by student in time t=16+ distance travelled by bus in time t. ⇒vt=16+(ut+
1
2
at2) ⇒vt=16+0×t+
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2
×9×t2
⇒vt=16+
9
2
t2⇒9t2−2vt+32=0
The above equation must have real roots. i.e its discriminant ≥0 i.e (2v)2−4×9×32≥0 ⇒4v2−4×288≥0⇒v2−288≥0 ⇒v2≥288. v≥12√2m∕s Minimum velocity of student to catch the bus =12√2m∕s=α√2m/s (given) ∴α=12
