Physics question?

Since the force is causing the car’s velocity to decrease to 0 m/s, the direction of the force must be in the opposite direction of the motion of the car. The first thing that we need to do is convert the car’s velocity from km/s to m/s.

1 km = 1000 m, 1 h = 3600 s, 1 km/h = 1000/3600 = 5/18 m/s

To convert the velocity from km/h to m/s, multiply by 5/18.

v = 100 * 5/18 = 250/9

This is 27 and 7/9th m/s.

Let’s use this number in the following equation to determine the acceleration.

vf^2 = vi^2 + 2 * a * d, vf = 0, vi = 250/9, d = 50

0 = (250/9)^2 + 2 * a * 50

a = (250/9)^2 ÷ -100 = -7.716049383 m/s

To determine the force, multiply by the mass.

F = -1000 * -7.716049383 = -7,716.049383 N

The negative sign means the force is in the opposite direction of the motion of the car.

To answer this question you need to find the resultant acceleration due to the brakes.

We know that the car is traveling at 27.78 ms^-1 (100*1000/3600) before the brakes are applied, and we know its final velocity is 0. Using v^2=u^2+2a*s, we can solve for the acceleration. Then we can use F=ma to find the force.

v^2=u^2+2as

0=(27.7)^2 +2*a*50

After algebraic steps, a works out to be 7.71 ms^-2

F=ma

F=1000*7.71 =7710 N

The direction of the force would be south since it acts in an opposite direction to the motion of the car (in order to slow it down).

x=v0t-1/2at^2

v=v0-at

when tha car stops v=0 then t=v0/a

replacing t into the first eq. on get

x=v0^2/(2a)

then

a=v0^2/(2x)

a=(100/3.6)^2/(2*50)=7.716 m/s^2

F=ma=7716 N

same direction of initial speed but opposite versus