The body moves along an inclined plane with a length of L = 10 m with an acceleration a = 0.2 m

The body moves along an inclined plane with a length of L = 10 m with an acceleration a = 0.2 m / s2 and an initial speed V0 = 1.5 m / s. Find the time t of movement along this plane and the speed V at the end of the descent.

Task data: L (length of the inclined plane, distance traveled) = 10 m; a (acceleration) = 0.2 m / s2; V0 (initial velocity of the taken body) = 1.5 m / s.

1) Let’s compose and solve the quadratic equation to determine the time of movement: S = V0 * t + 0.5 * a * t².

0.5 * a * t² + V0 * t – S = 0.

0.5 * 0.2 * t² + 1.5 * t – 10 = 0.

0.1t² + 1.5t – 10 = 0 | * ten.

t² + 15t – 100 = 0 | * ten.

By Vieta’s theorem: t1 = 5 s (true); t2 = -20 s (not true).

2) Speed at the end of the descent: V = V0 + a * t = 1.5 + 0.2 * 5 = 2.5 m / s.