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A car engine produces a force of 2,329 N on a car of mass 858 kg that is initially at rest. What will the speed of the car be after a distance of 159 m, in units of m/s?

Answer :

To find the speed of the car after a distance of 159 m, we can use Newton's second law of motion and the kinematic equation. By calculating the acceleration using the given force and mass, we can then determine the final speed of the car to be approximately 29.42 m/s.

To find the speed of the car, we can use Newton's second law of motion which states that force equals mass multiplied by acceleration. In this case, the force produced by the car engine is 2,329 N and the mass of the car is 858 kg. The acceleration can be found by dividing the force by the mass. After finding the acceleration, we can use the kinematic equation v^2 = u^2 + 2as to find the final speed of the car after a distance of 159 m.

Using the calculated acceleration, we can rearrange the kinematic equation to solve for the final speed:

v^2 = u^2 + 2as

where v is the final speed, u is the initial speed (which is 0 since the car is initially at rest), a is the acceleration, and s is the distance.

Plugging in the values,

v^2 = 0 + 2(acceleration)(distance)

Now, we can calculate the acceleration by dividing the force by the mass:

acceleration = force / mass = 2329 / 858 = 2.71 m/s^2

Substituting the values back into the equation:

v^2 = 2(2.71)(159)

Simplifying the equation:

v^2 = 2(2.71)(159)

v^2 = 866.12

Taking the square root of both sides to solve for v:

v = √866.12

v ≈ 29.42 m/s

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