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A car starts from rest and begins moving on a road. It encounters 1000 N of air resistance and 11,000 N of applied force from floor to the tires on the car. During this motion, the car is accelerating at a rate of 5.5 m/s². What is the car’s mass? How fast is the car going 10s later? How far did it travel in this time period? Draw the x-t graph and v-t graph for this motion and system schema and FBD!

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Final answer:

The car's mass is 1818.18 kg. After 10 seconds, the car is moving at 55 m/s, and it has traveled 275 meters. The x-t graph for this motion would curve upward, while the v-t graph would have a linear, positive slope representing constant acceleration.

Step-by-step explanation:

The question involves finding the mass of a car, its velocity after 10 seconds, and the distance it has traveled in that time using the given forces and acceleration.

To Find the Car's Mass:

Use Newton's second law of motion (F = ma) to find the mass. The net force is the difference between the applied force and air resistance.

  • Net force (Fnet) = Applied force - Air resistance = 11,000 N - 1,000 N = 10,000 N
  • Acceleration (a) = 5.5 m/s2
  • Mass (m) = Fnet / a = 10,000 N / 5.5 m/s2 = 1818.18 kg

To Find the Velocity after 10 seconds:

Velocity (v) = Initial velocity (u) + (Acceleration (a) * time (t)), where u = 0 (starts from rest).

  • v = 0 + (5.5 m/s2 * 10 s) = 55 m/s

To Find the Distance Traveled in 10 seconds:

Using the formula s = ut + (1/2)at2, where u = 0 (starts from rest).

  • Distance (s) = 0 + (1/2) * 5.5 m/s2 * (10 s)2 = 275 m

The x-t graph would show a curve starting at the origin and getting steeper, as the car is accelerating. The v-t graph would show a straight line starting at the origin and having a positive slope equal to the acceleration of 5.5 m/s2.

The free-body diagram (FBD) would include arrows representing applied force and air resistance, with a greater length arrow for the applied force since it's larger than the air resistance.

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