The body from the state of rest moved with an acceleration of 4 m / s². Determine the path of the body

The body from the state of rest moved with an acceleration of 4 m / s². Determine the path of the body in the fifth second of movement.

V0 = 0 m / s.

a = 4 m / s ^ 2.

t1 = 4 s.

t2 = 5 s.

S -?

The displacement of the body S in the fifth second is found by the formula: S = S5 – S4, where S5 is the displacement of the body in five seconds (t2 = 5 s), S4 is the displacement of the body in four seconds (t1 = 4 s).

The movement of the body S with an initial zero speed V0 = 0 m / s with uniformly accelerated motion is expressed by the formula: S = a * t ^ 2/2, where a is the body’s acceleration, t is the time of movement.

S5 = a * t2 ^ 2/2.

S4 = a * t1 ^ 2/2.

S = a * t2 ^ 2/2 – a * t1 ^ 2/2 = a * (t2 ^ 2 – t1 ^ 2) / 2.

S = 4 m / s ^ 2 * ((5 s) ^ 2 – (4 s) ^ 2) / 2 = 18 m.

Answer: the body in the fifth second passes the path S = 18 m.