Answer to Question #92542 in Mechanics | Relativity for m

Question

The acceleration of a point is given by a=5-t^2. write an equation for velocity if v=4 m/s when t=3 s

Answer 1

Velocity of the point

$$v(t)=\int a(t)dt=\int (5-t^2)dt=5t-\frac{t^3}{3}+v_0$$

$$v(3)=5\times 3-\frac{3^3}{3}+v_0=4$$

$$v_0=-2 \:\rm{m/s}$$

Finally, the equation for velocity

$$v(t)=5t-\frac{t^3}{3}-2$$