Question

A particle starts from the origin of coordinates at time t= 0 and moves in the xy plane with a constant acceleration αin the y-direction. Its equation of motion is y = βx². Its velocity component in the x- direction is

• A. Variable
• B. $\sqrt{\frac{2\alpha}{\beta}}$
• C. $\frac{\alpha}{2\beta}$
• D. $\sqrt{\frac{\alpha}{2\beta}}$

Answer 1

Answer: (D)

$\sqrt{\frac{\alpha}{2\beta}}$

Answer 2

y = βx² or y = 2βx $\overset{\bullet}{x}$

or $\overset{\bullet \bullet}{y}$ = 2β($\overset{\bullet}{x}$)² = α

or $\overset{\bullet}{x}$ = $\sqrt{\frac{\alpha}{2\beta}}$

[$\overset{\bullet \bullet}{x}$ = 0 as it has acceleration only in the y – direction.]