Answer :
acceleration is taken as constant
we know a = dv/dt
dv = a dt
Integrating both sides with proper limits
[tex] \int\limits^u_v \, dv= \int\limits^0_t {a} \, dt[/tex]
[tex] \int\limits^u_v \, dv=a \int\limits^0_t \, dt[/tex]
[tex][v]^v_u=a[t]^t_0[/tex]
[tex]v-u=at[/tex]
[tex]v=u+at[/tex]
second equation
a= dv/dt x dx/dx
a = v dv/dx
v dv = a dx
Integrating both sides with proper limits
[tex]\int\limits^v_u {v} \, dv = \int\limits^s_0 {a} \, dx[/tex]
[tex]\int\limits^v_u {v} \, dv =[/tex]
[tex][\frac{v^2}{2}]^v_u =a[x]^s_0 [/tex]
[tex] v^{2}-u^{2} = 2as[/tex]
we know a = dv/dt
dv = a dt
Integrating both sides with proper limits
[tex] \int\limits^u_v \, dv= \int\limits^0_t {a} \, dt[/tex]
[tex] \int\limits^u_v \, dv=a \int\limits^0_t \, dt[/tex]
[tex][v]^v_u=a[t]^t_0[/tex]
[tex]v-u=at[/tex]
[tex]v=u+at[/tex]
second equation
a= dv/dt x dx/dx
a = v dv/dx
v dv = a dx
Integrating both sides with proper limits
[tex]\int\limits^v_u {v} \, dv = \int\limits^s_0 {a} \, dx[/tex]
[tex]\int\limits^v_u {v} \, dv =[/tex]
[tex][\frac{v^2}{2}]^v_u =a[x]^s_0 [/tex]
[tex] v^{2}-u^{2} = 2as[/tex]
