Question

A particle starts flying in the xy-plane with a speed of $2\widehat{i} + 5x\widehat{j}$. Initial position of the particle was the origin (0, 0) of the plane. The trajectory of the particle is represented by the equation –

• A. y = 1.25 x²
• B. y = 5x²
• C. y = 2.5 x²
• D. x = 5y²

Answer 1

Answer: (A)

y = 1.25 x²

Answer 2

Q v_x = $\frac { \mathrm { dx } } { \mathrm { dt } }$ = 2 m/s

̃ x = 2t …..(i)

also, v_y = $\frac { \mathrm { dy } } { \mathrm { dt } }$ = 5x

̃ dy = xdt = 5(2t)dt from eq. (i)

̃ dy = 10t dt

̃ y = $\frac { 10 \mathrm { t } ^ { 2 } } { 2 }$ = 5t² …….(ii)

From (i) and (ii)

y = 5 (x/2)²

̃ y = $\frac { 5 } { 4 }$ x²