Question

A particle moves with a uniform speed of 2 m/s in x – y plane according to the equation y = 4x², where x and y are in metre. The acceleration of the particle along y-axis while passing through the origin has magnitude

	2 m/s2
	4 m/s2
	16 m/s2
	32 m/s2

Answer 1

Dear student,

$$\begin{gathered} consideringtheparticleismovingwithuniformspeed2m/salongxaxis \\ wecanwrite \\ {v}_x=2m/s \\ now,v_x=\frac{dx}{dt} \\ dx=v_{x}dt \\ \int dx=\int v_{x}dt=\int 2dt \\ x=2t \\ again, \\ y=4x^2=4{\left(2t\right)}^2=16t^2 \\ thenspeedalongyaxiscanbewrittenas \\ {v}_y=\frac{dy}{dt}=\frac{d\left(16t^2\right)}{dt}=32t \\ andacclerationalongyaxis \\ {a}_y=\frac{d{v}_y}{dt}=\frac{d\left(32t\right)}{dt}=32 \\ hence, \\ {a}_y=32m/s^2(option4) \end{gathered}$$
regards,