Moving uniformly and rectilinearly, the body increased its speed 3 times in 5 s.

Moving uniformly and rectilinearly, the body increased its speed 3 times in 5 s. The distance traveled during this time is 200 m. Determine the acceleration of the body.

Given: t (acceleration duration) = 5 s; V (final speed) = 3V0 (initial speed); S (covered in 5 s) = 200 m; a = const.

The acceleration of the body is determined from the formulas for calculating the distance traveled and speed.

a) S = (V ^ 2 – V0 ^ 2) / 2a, whence a = (V ^ – V0 ^ 2) / 2S = ((3V0) ^ 2 – V0 ^ 2) / 2S = 8V0 ^ 2 / 2S = 4V0 ^ 2 / S.

b) V = V0 + a * t, whence a = (V – V0) / t = 2V0 / t.

Initial speed: 4V02 / S = 2V0 / t and V0 = S / 2t = 200 / (2 * 5) = 20 m / s.

Acceleration: a = 2 * 20/5 = 4 * 202/200 = 8 m / s2.