The initial velocityof a particle along x axis is u at t=0 x=0 and its acceleration is given by a =2x then whats the correct equation for v^2= u^2 +2as

v² = u² + 2x²

Explanation:

v² = u² + 2as is only valid for constant acceleration.  Here, the acceleration is a function of position.  We can find the function of velocity by integrating.  Acceleration is the derivative of velocity with respect to time:

a = 2x

dv/dt = 2x

Apply chain rule:

dv/dt = dx/dt × dv/dx

dv/dt = v × dv/dx

Therefore:

v dv/dx = 2x

Separate the variables and integrate:

v dv = 2x dx

½ v² |ᵤᵛ = x² |₀ˣ

½ (v² − u²) = x²

v² − u² = 2x²

v² = u² + 2x²

if they have a finite resultant

i had this question and the answer was 3.15 miles.

martina travels from school to her mom's office. from there, she walks to school. after school, she walks to the library and then to a friends house before finally ending back at home. find martina's total distance traveled.

a) 0 miles  

b) 0.4 miles  

c) 1 mile  

d) 3.15 miles