Question

A car in accelerated motion along the line ox moves from position x1 and x2 respectively on time t1 and t2 prove that the acceleration of a car is given by

a=2(x2t1-x1t2)/t1t2(t1-t2)

Answer 1

$$x_1=vt_1+0.5at_1^2$$

$$x_2=vt_2+0.5at_2^2$$

$$v=\frac{x_1}{t_1}-0.5at_1$$

Thus,

$$x_2=\left(\frac{x_1}{t_1}-0.5at_1\right)t_2+0.5at_2^2$$

$$a=\frac{2(x_2t_1-x_1t_2)}{t_1t_2(t_1-t_2)}$$