Question

Велосипедист массой 50 кг движется по прямолинейному участку горизонтального шоссе согласно управлению х=4+2t+t². Какую работу выполняет велосипедист за 20 с движения ?​

Answer 1

T=20 x=4+2*20+20*20=444. S= 444-4=440м
а=2м/с2 F=ma=50*2=100H A=F*S=100*440

Answer 2

Calculation of Work Done by the Cyclist

To calculate the work done by the cyclist, we need to determine the force exerted by the cyclist and the displacement of the cyclist. The work done is given by the formula:

Work = Force x Displacement x cos(theta)

In this case, since the cyclist is moving along a straight line on a horizontal road, the angle between the force and displacement vectors is 0 degrees, so cos(theta) = 1.

The force exerted by the cyclist can be calculated using Newton's second law:

Force = mass x acceleration

Given that the mass of the cyclist is 50 kg, we need to find the acceleration. The equation of motion for the cyclist is given as:

x = 4 + 2t + t^2

where x is the position of the cyclist and t is the time.

To find the acceleration, we need to differentiate the equation of motion with respect to time:

a = d^2x/dt^2

Differentiating the equation of motion, we get:

a = 2

Now we can calculate the force:

Force = mass x acceleration = 50 kg x 2 m/s^2 = 100 N

The displacement of the cyclist can be calculated by substituting the time t = 20 s into the equation of motion:

x = 4 + 2t + t^2 = 4 + 2(20) + (20)^2 = 4 + 40 + 400 = 444 m

Now we can calculate the work done:

Work = Force x Displacement = 100 N x 444 m = 44,400 J

Therefore, the cyclist performs 44,400 Joules of work during the 20 seconds of motion.