The car moves in a straight line and uniformly accelerated and for a time interval of 40 s covers a distance of 800 m.

The car moves in a straight line and uniformly accelerated and for a time interval of 40 s covers a distance of 800 m. If the vehicle speed module during this time has increased 3 times, then the acceleration module is equal.

Initial data: t (specified time interval) = 40 s; S (distance traveled by the car during time t) = 800 m; V = 3V0 (vehicle speed module increased 3 times).

1) We transform the formula for the traversed path:

S = (V ^ 2 – V0 ^ 2) / 2a = (9V0 ^ 2 – V0 ^ 2) / 2a = 4V0 / a.

2) Determine the initial speed:

V = V0 + a * t; a * t = V – V0 = 2V0; V0 = 0.5a * t.

3) Let’s define the acceleration of the body:

S = 4V0 / a = 4 * (0.5a * t) ^ 2 / a = 4 * 0.25 * a ^ 2 * t ^ 2 / a = a * t ^ 2.

a = S / t ^ 2 = 800/40 ^ 2 = 0.5 m / s ^ 2.