Question

a 800 kg roller coaster cart is accelerated by a constant net force over a distance of 10 meters, as shown in the graph below: determine the speed of the cart after being accelerated for 10.0 meters.

Answer 1

(A) 22.4 m/s

Explanation: hope this helps !

Answer 2

vf = 22.36[m/s]

Step-by-step explanation:

First we must understand the data given in the problem:

m = mass = 800 [kg]

F = force = 20000[N]

dx = displacement = 10[m]

From newton's second we know that the sum of forces must be equal to the product of mass by acceleration.

`F = m*a\\20000 = 800*a\\a = 20000/800\\a = 25 [m/s^2]`

With the calculated acceleration, we can use the kinematics equations.

`v_(f) ^(2) =v_(o) ^(2)+2*a*dx\\ v_(o) = initial velocity = 0\\a = acceleration = 25[m/s^2]\\dx= displacement = 10[m]\\`

The key to using this equation is to clarify that the initial velocity is zero since the body is at rest, otherwise the initial velocity would be an initial data.

`v_(f) =√(2*25*10) \\v_(f) =22.36[m/s]`

Another way of solving this problem is by means of the definition of work and kinetic energy, where work is defined as the product of the force by the distance.

W =F*d

W = 20000*10

W = 200000[J]

Kinetic energy is equal to work, therefore the value calculated above is equal to:

`E_(k)=W =0.5*m*v_(f)^(2) \\200000=0.5*800*v_(f)^(2)\\v_(f)=\sqrt{(200000)/(0.5*800) } \\v_(f)=22.36[m/s]`