A 1000-kg car traveling with a speed of 35 m/s skids to a stop in 25m. Determine the average force applied to the breaks. If it took 3.2s to stop, who much power was generated by the breaks?

1. 24500 N.

2. 191406.25 watt

Explanation:

From the question given above, the following data were obtained:

Mass (m) of car = 1000 Kg

Initial velocity (u) = 35 m/s

Distance (s) = 25 m

Final velocity (v) = 0 m/s

Time (t) = 3.2 s

Force (F) =?

Power (P) =?

Next, we shall determine the acceleration of the car. This can be obtained as follow:

Initial velocity (u) = 35 m/s

Distance (s) = 25 m

Final velocity (v) = 0 m/s

Acceleration (a) =?

v² = u² + 2as

0 = 35² + (2 × a × 25)

0 = 1225 + 50a

Collect like terms

0 – 1225 = 50a

– 1225 = 50a

Divide both side by 50

a = – 1225 / 50

a = –24.5 m/s²

1. Determination of the force.

Mass (m) of car = 1000 Kg

Acceleration (a) = –24.5 m/s²

Force (F) =?

F = m × a

F = 1000 × –24.5

F = –24500 N

The negative sign indicate that the force is in opposite direction to the motion of the car.

2. Determination of the power

Force (F) = 24500 N

Distance (s) = 25 m

Time (t) = 3.2 s

Power (P) =?

Next, we shall determine the energy.

Energy = force × distance

Energy = 24500 × 25

Energy = 612500 J

Finally, we shall determine the power. This is illustrated below:

Power = Energy /time

Power = 612500 /3.2

Power = 191406.25 watt