Question

Define (i) v = u + at (ii) V2 – u2 = 2as by calculus method

CLASS - XI PHYSICS (Kinematics)

Answer 1

 acceleration is taken as constant
we know a = dv/dt
                 dv = a dt   
  Integrating both sides with proper limits 

$\int\limits^u_v \, dv= \int\limits^0_t {a} \, dt$

$\int\limits^u_v \, dv=a \int\limits^0_t  \, dt$

$[v]^v_u=a[t]^t_0$

$v-u=at$

$v=u+at$

second equation

a= dv/dt x dx/dx
a = v dv/dx
v dv = a dx 

  Integrating both sides with proper limits 

$\int\limits^v_u {v} \, dv = \int\limits^s_0 {a} \, dx$

$\int\limits^v_u {v} \, dv =$


$[\frac{v^2}{2}]^v_u =a[x]^s_0$

$v^{2}-u^{2} = 2as$

Answer 2

The answer is provided in the attachment