Question

Two cars start in a race with velocities and
u, and travel in a straight line with
accelerations a' and . If both reach the
finish line at the same time, the range of the
race is​

Answer 1

Let distance covered by cars = L and time taken is t

Let distance covered by cars = L and time taken is t For first car :- initial velocity = v₁

Let distance covered by cars = L and time taken is t For first car :- initial velocity = v₁Acceleration = a₁

Let distance covered by cars = L and time taken is t For first car :- initial velocity = v₁Acceleration = a₁Time taken = t

Let distance covered by cars = L and time taken is t For first car :- initial velocity = v₁Acceleration = a₁Time taken = t ∴use formula S = ut + 1/2at²

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2),

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t²

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²t = 2(v₁ - v₂)/(a₂ - a₁) , put it in equation (1)

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²t = 2(v₁ - v₂)/(a₂ - a₁) , put it in equation (1) L = v₁[2(v₁ - v₂)/(a₂ - a₁)] + 1/2a₁[2(v₁ - v₂)/(a₂ - a₁)]²

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²t = 2(v₁ - v₂)/(a₂ - a₁) , put it in equation (1) L = v₁[2(v₁ - v₂)/(a₂ - a₁)] + 1/2a₁[2(v₁ - v₂)/(a₂ - a₁)]² = (v₁ - v₂)/(a₂ - a₁)[2v₁ + 2a₁(v₁ - v₂)/(a₂ - a₁)]

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²t = 2(v₁ - v₂)/(a₂ - a₁) , put it in equation (1) L = v₁[2(v₁ - v₂)/(a₂ - a₁)] + 1/2a₁[2(v₁ - v₂)/(a₂ - a₁)]² = (v₁ - v₂)/(a₂ - a₁)[2v₁ + 2a₁(v₁ - v₂)/(a₂ - a₁)] = (v₁ - v₂)/(a₂ - a₁) [2v₁(a₂ - a₁) + 2a₁(v₁ - v₂)]/(a₂ - a₁)

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²t = 2(v₁ - v₂)/(a₂ - a₁) , put it in equation (1) L = v₁[2(v₁ - v₂)/(a₂ - a₁)] + 1/2a₁[2(v₁ - v₂)/(a₂ - a₁)]² = (v₁ - v₂)/(a₂ - a₁)[2v₁ + 2a₁(v₁ - v₂)/(a₂ - a₁)] = (v₁ - v₂)/(a₂ - a₁) [2v₁(a₂ - a₁) + 2a₁(v₁ - v₂)]/(a₂ - a₁)= (v₁ - v₂)/(a₂ - a₁)² [2v₁a₂ - 2v₁a₁ + 2v₁a₁ -2a₁v₂]

formula S = ut + 1/2at² L = v₁t + 1/2 a₁t² --------(1)For 2nd car :- initial velocity = v₂acceleration = a₂time taken = t so, L = v₂t + 1/2 a₂t² -----(2)From equations (1) and (2), v₁t + 1/2a₁t² = v₂t + 1/2a₂t² (v₁ - v₂)t = 1/2(a₂ - a₁)t²t = 2(v₁ - v₂)/(a₂ - a₁) , put it in equation (1) L = v₁[2(v₁ - v₂)/(a₂ - a₁)] + 1/2a₁[2(v₁ - v₂)/(a₂ - a₁)]² = (v₁ - v₂)/(a₂ - a₁)[2v₁ + 2a₁(v₁ - v₂)/(a₂ - a₁)] = (v₁ - v₂)/(a₂ - a₁) [2v₁(a₂ - a₁) + 2a₁(v₁ - v₂)]/(a₂ - a₁)= (v₁ - v₂)/(a₂ - a₁)² [2v₁a₂ - 2v₁a₁ + 2v₁a₁ -2a₁v₂]= 2(v₁ - v₂)(v₁a₂ - a₁v₂)/(a₂ - a₁)²