Question

Из пункта А выехал грузовик с постоянной скоростью 72 км/ч. Одновременно с ним из пункта В, отстоящего от А на расстоянии 1,5 км, начал двигаться мотоциклист. Считая движение мотоциклиста равноускоренным с a=2 м/с2, определить, через которое мотоциклист догонит грузовик, и путь, пройденный каждым из них до встречи.

Answer 1

S мотоциклиста = (а*t^2)/2=(2t^2)/2=t^2 м
v грузовика=75 км/ч=20 м/с
s грузовика=v*t=20t м/с
s мотоциклиста+s грузовика=s между пунктами
t^2+20t=1500
t^2+20t-1500=0
t=30 с - время до встречи
30^2=900 м - проехал мотоциклист
30*20=600 м - проехал грузовик

Answer 2

Problem Setup

A truck travels from point A at a constant speed of 72 km/h. Simultaneously, a motorcyclist starts moving from point B, which is 1.5 km away from point A. The motorcyclist's motion is considered uniformly accelerated with an acceleration of a=2 m/s^2. We need to determine the time it takes for the motorcyclist to catch up to the truck and the distance each of them covers until they meet.

Calculating the Time to Catch Up

To find the time it takes for the motorcyclist to catch up to the truck, we can use the following kinematic equation: v = u + at Where: - v = final velocity - u = initial velocity - a = acceleration - t = time

The initial velocity of the motorcyclist, u, can be calculated using the formula: u = 0 This is because the motorcyclist starts from rest.

The final velocity of the motorcyclist, v, can be calculated using the formula: v = u + at

Calculating the Distance Covered

To calculate the distance covered by each vehicle, we can use the following kinematic equation: s = ut + (1/2)at^2 Where: - s = distance - u = initial velocity - t = time - a = acceleration

We can use this equation to find the distance covered by the truck and the motorcyclist until they meet.

Let's calculate the time it takes for the motorcyclist to catch up to the truck and the distance each of them covers until they meet.