Question

How large a net force is required to accelerate a 1,586-kg SUV from rest to a speed of 10.4 m/s in a distance of 212 m?

Answer 1

F = 404.6 N

Step-by-step explanation:

Mechanical Force

According to the second Newton's law, the net force exerted by an external agent on an object of mass m is:

F = m.a

Where a is the acceleration of the object.

On the other hand, the equations of the Kinematics describe the motion of the object by the equation:

`v_f=v_o+a.t`

Where:

vf is the final speed

vo is the initial speed

a is the acceleration

t is the time

Another useful equation for speeds and distance X is:

`V_f^2=V_o^2+2aX`

To calculate the acceleration, we solve for a:

`\displaystyle a=(V_f^2-V_o^2)/(2X)`

The SUV starts from rest (vo=0) to vf=10.4 m/s traveling a distance of X=211 m, thus the acceleration is:

`\displaystyle a=(10.4^2-0^2)/(2(212))`

`\displaystyle a=(108.16)/(424)`

`a=0.26 \ m/s^2`

The force needed to accelerate the SUV of mass m=1,586 Kg is:

F = 1,586*0.26

F = 404.6 N