A 2.0×103 kg car accelerates from rest under

the action of two forces. One is a forward
force of 1153 N provided by traction between
the wheels and the road. The other is a 939 N resistive force due to various frictional forces.
How far must the car travel for its speed to
reach 2.0 m/s?
Answer in units of m.

One step at a time.

First compute the net force acting:
F = 1153 - 939 = 214 N

Then compute the acceleration rate a using
F = m a; a = F/m

Then compute the time t required to reach velocity V:
t = V/a

The distance travelled is
X = (1/2) a t^2

To find the distance the car must travel, we can use the concepts of force, mass, and acceleration.

First, let's calculate the net force acting on the car. Net force is the difference between the forward force and the resistive force:

Net Force = Forward Force - Resistive Force

Given:
Forward Force = 1153 N
Resistive Force = 939 N

Substituting the values:

Net Force = 1153 N - 939 N
Net Force = 214 N

Next, let's calculate the acceleration of the car using Newton's second law of motion, which states that the net force applied to an object is equal to the mass of the object multiplied by its acceleration:

Net Force = Mass × Acceleration

Given:
Mass of the car = 2.0 × 10^3 kg

Rearranging the formula to solve for acceleration:

Acceleration = Net Force / Mass

Substituting the values:

Acceleration = 214 N / 2.0 × 10^3 kg
Acceleration = 0.107 m/s^2

We know that acceleration can be calculated using the following equation:

Acceleration = (Change in Velocity) / Time

In this case, the car starts from rest (0 m/s) and reaches a speed of 2.0 m/s. Let's find the change in velocity:

Change in Velocity = Final Velocity - Initial Velocity
Change in Velocity = 2.0 m/s - 0 m/s
Change in Velocity = 2.0 m/s

Now, we need to find the time it takes for the car to reach this velocity. Rearranging the second equation of motion:

Time = (Change in Velocity) / Acceleration

Substituting the values:

Time = 2.0 m/s / 0.107 m/s^2
Time ≈ 18.69 s

Finally, we can find the distance traveled by the car using the formula:

Distance = (Initial Velocity × Time) + (0.5 × Acceleration × Time^2)

Since the initial velocity is 0 m/s:

Distance = (0.5 × Acceleration × Time^2)

Substituting the values:

Distance = 0.5 × 0.107 m/s^2 × (18.69 s)^2
Distance = 0.5 × 0.107 m/s^2 × 348.5841 s^2
Distance ≈ 20.99 m

Therefore, the car must travel approximately 20.99 meters for its speed to reach 2.0 m/s.