A 2.3 × 103 kg car accelerates from rest under the action of two forces. One is a forward force of 1141 N provided by traction between the wheels and the road. The other is a 947 N resistive force due to various frictional forces.

How far must the car travel for its speed to reach 3.0 m/s?

a = (F1-F2)/m

F1 = 1141 N.
F2 = 947 N.
M = 2300 kg
Solve for a.

V^2 = Vo^2 + 2a*d

V = 3 m/s.
Vo = 0
a: Calculated in step #1.
Solve for d in meters.
.

To find the distance the car must travel, we can use the equations of motion. Let's break down the problem and use the equations to solve it step by step.

Given data:
Mass of the car (m) = 2.3 × 10^3 kg
Forward force (Ff) = 1141 N
Resistive force (Fr) = 947 N
Final speed (v) = 3.0 m/s

Step 1: Calculate the net force acting on the car.
Since we have two forces acting on the car in opposite directions, we can find the net force by subtracting the resistive force (Fr) from the forward force (Ff).
Net force (Fnet) = Ff - Fr

Substituting the values of the given forces:
Fnet = 1141 N - 947 N
Fnet = 194 N

Step 2: Use Newton's second law of motion to find the acceleration of the car.
Newton's second law states that the net force acting on an object is equal to the mass of the object times its acceleration.
Fnet = m * a

Rearranging the equation:
a = Fnet / m

Substituting the known values:
a = 194 N / 2.3 × 10^3 kg
a ≈ 0.0843 m/s²

Step 3: Use the kinematic equation to find the distance traveled by the car.
The kinematic equation relating final velocity, initial velocity, acceleration, and displacement is:
v² = u² + 2as

Here, the car is starting from rest (u = 0 m/s).

Rearranging the equation:
2as = v²
s = v² / (2a)

Substituting the known values:
s = (3.0 m/s)² / (2 × 0.0843 m/s²)
s ≈ 52.83 m

Therefore, the car must travel approximately 52.83 meters to reach a speed of 3.0 m/s.