Question

Грузовой автомобиль при аварийном торможении движется с ускорением а= 5 м/с в квадрате, определите путь,проходимый автомобилем при аварийном торможении,если он двигался со скоростью v=72 км/ч

Answer 1

Воспользуемся двумя формулами: s=v0t-at^2*1/2
v=v0-at
v0=72 км/ч= 20м/с
v=0 км/ч
найдем время: v=v0-at =>v0=at => t=v0/a
s =vo*v0/a - 1/2*a*(v0/a)^2 => S= V0^2-1/2*v0^2/a =>s= (v0^2*a-0.5v0^2)/a =>
s=v0^2(a-0.5)/a= (20^2 * 4.5)/5 = 360

Answer 2

Calculation of the Stopping Distance of a Truck

To calculate the stopping distance of a truck during emergency braking, we need to use the equation of motion:

\[s = \frac{v^2}{2a}\]

Where: - s is the stopping distance - v is the initial velocity of the truck - a is the deceleration (negative acceleration) of the truck during emergency braking

Given that the truck is moving with an acceleration of a = 5 m/s^2 and an initial velocity of v = 72 km/h, we need to convert the velocity to meters per second:

\[v = 72 \, \text{km/h} = \frac{72 \times 1000}{3600} \, \text{m/s} = 20 \, \text{m/s}\]

Now we can substitute the values into the equation to calculate the stopping distance:

\[s = \frac{(20 \, \text{m/s})^2}{2 \times (-5 \, \text{m/s}^2)}\]

Simplifying the equation:

\[s = \frac{400 \, \text{m}^2/\text{s}^2}{-10 \, \text{m/s}^2} = -40 \, \text{m}\]

The negative sign indicates that the stopping distance is in the opposite direction of the truck's motion. However, in this context, we can consider the magnitude of the stopping distance, which is 40 meters.

Therefore, the truck will travel a distance of 40 meters during emergency braking.