Question

select the correct path equation
Particle having positions as
y=6t and X=3t^2
​

Answer 1

The velocity and acceleration can never be zero.

Explanation:

We are given that:

• x = 3 t² - 6 t   me          
• y = t² - 2 t   m

x = 3 t (t - 2)   m  , y = t (t - 2)  m

x = 3 y

Angle made with x axis = Tan⁻¹ (1/3) 

V (x)  = 6 t - 6    m/s              v (y) = 2 t - 2      m/s

V (x) = 3 v (y)

Angle made by velocity with x axis :  Tan⁻¹ (1/3)

a (x)  = 6   m/s^2                   a_y = 2   m/s^2

a(x) = 3  a (y)

Angle made by acceleration with x axis = Tan⁻¹ (1 / 3)

a (x,y) = √(36+4)  = 2√10  m/sec^2    

As we know that acceleration is never zero.

V (x,y,t) = √(v²_x +v²_y) = √10 v(y)

V (x,y,t)  = 2 √10 (t - 1)   m/s

Velocity is zero  at   t = 1 sec

V (t=2 sec) = 2√10 m/s

At t = 2 sec, the velocity and acceleration vectors are parallel., as angles made by them with x axis are same