Question

Мимо остановки по прямой улице проезжает грузовик со скоростью 10м/с. Через 5с от остановки вдогонку грузовику отъезжает мотоциклист, движущийся с ускорением 3 м/с^2. Чему равна скорость мотоциклиста в момент, когда он догонит грузовик?

Answer 1

s1=v(t+5)

s2=at^2/2

v(t+5)=at^2/2

2vt+10v=at^2

2*10t+10*10=3t^2

3t^2-20t-100=0

D=100+300=400

t1=(10+20)/3=10 (с) - двигался мотоциклист

t2=(10-20)/3<0

v=v0+at

v=0+3*10=30(м/с)

Ответ: 30 м/с

Answer 2

Problem Analysis

We are given that a truck is moving with a constant speed of 10 m/s along a straight road. After 5 seconds, a motorcyclist starts chasing the truck with an acceleration of 3 m/s^2. We need to determine the speed of the motorcyclist when they catch up to the truck.

Solution

To solve this problem, we can use the equations of motion. The equation that relates displacement, initial velocity, acceleration, and time is:

s = ut + (1/2)at^2

where: - s is the displacement - u is the initial velocity - a is the acceleration - t is the time

In this case, the displacement of the motorcyclist is the same as the displacement of the truck when they catch up. Let's assume that the motorcyclist catches up to the truck after time t.

For the truck: - Initial velocity (u) = 10 m/s - Acceleration (a) = 0 (since the truck is moving with a constant speed) - Time (t) = t

For the motorcyclist: - Initial velocity (u) = 0 (since the motorcyclist starts from rest) - Acceleration (a) = 3 m/s^2 - Time (t) = t - 5 (since the motorcyclist starts chasing the truck after 5 seconds)

Setting the displacements equal to each other, we can solve for t:

10t = (1/2)(3)(t - 5)^2

Simplifying the equation:

10t = (3/2)(t^2 - 10t + 25)

20t = 3t^2 - 30t + 75

3t^2 - 50t + 75 = 0

Solving this quadratic equation, we find two possible values for t. We can discard the negative value since time cannot be negative. Therefore, we have:

t = 5 seconds

Now, we can find the speed of the motorcyclist at this time. Using the equation of motion:

v = u + at

For the motorcyclist: - Initial velocity (u) = 0 - Acceleration (a) = 3 m/s^2 - Time (t) = 5 seconds

Substituting the values:

v = 0 + (3)(5)

v = 15 m/s

Therefore, the speed of the motorcyclist when they catch up to the truck is 15 m/s.

Answer

The speed of the motorcyclist in the moment when they catch up to the truck is 15 m/s.