1.2.3 | revision #13307 | Savchenko Solutions

Statement

1.2.3. A body for time $$t_0$$ moves with constant velocity $$v_0$$ . Then its velocity increases linearly with time so that at time $$2 t_0$$ it is equal to $$2 v_0$$ . Determine the path traveled by the body for time $$t > t_0$$ .

Solution

At time $$t_0$$ , the coordinate was $$x_1=v_0t_0$$ .
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On the interval from $$t_0$$ to $$2t_0$$ , the acceleration is constant and equal to $a=\frac{v_0}{t_0}$ .

In the case of equiaxcelerated motion with initial velocity $$v_0$$ from time $$t_0$$ , the path is found as

$x_2 = v_0 (t-t_0)+\frac{a(t-t_0)^2}{2}$

$$$x = x_1+x_2$$$

$x = v_0 t+\frac{a(t-t_0)^2}{2}$

Answer

$L = v_{0}t + \frac{v_{0} (t − t_{0})^{2}}{2t_{0}}$