Question

2. Швидкість тіла змінюється за законом υ = 20 – 1,5t. Знайти силу, що діє на тіло, якщо його маса 2 кг. Як рухається це тіло?

Answer 1

Given Information

The velocity of an object changes according to the law υ = 20 – 1.5t. The mass of the object is 2 kg. We need to find the force acting on the object and determine the nature of its motion.

Finding the Force Acting on the Object

To find the force acting on the object, we can use Newton's second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum. The momentum of an object is given by the product of its mass and velocity.

The formula for force (F) is given by: F = m * a where: - F = force - m = mass of the object - a = acceleration

Acceleration can be found by differentiating the velocity function with respect to time.

The velocity function is υ = 20 – 1.5t.

Differentiating υ with respect to t gives us the acceleration function a.

a = dυ/dt

Let's find the acceleration function a.

The derivative of υ = 20 – 1.5t with respect to t is -1.5.

So, the acceleration function a is -1.5 m/s^2.

Now, we can find the force acting on the object using the formula F = m * a.

Substituting the given mass m = 2 kg and acceleration a = -1.5 m/s^2 into the formula gives us:

F = 2 kg * (-1.5 m/s^2) F = -3 N

The force acting on the object is -3 N.

Nature of the Motion

The negative sign indicates that the force is acting in the opposite direction of the velocity. This means that the force is acting to decelerate the object.

Therefore, the object is moving with deceleration.

In summary, the force acting on the object is -3 N, and the object is moving with deceleration.