a (n) 1510 kg car is moving along a level road at 13.8 m/s. The driver accelerates and in the next 10s the engine provides 23400 J of additional energy. If 3900 J of this energy must be used to overcome friction, what is the final speed of the car?

To find the final speed of the car, we need to calculate the change in kinetic energy and use it to determine the new speed.

The change in kinetic energy can be calculated using the formula:

∆KE = KE_final - KE_initial

where KE is the kinetic energy.

The initial kinetic energy (KE_initial) of the car is given by:

KE_initial = (1/2) * m * v_initial^2
= (1/2) * 1510 kg * (13.8 m/s)^2

Next, we calculate the change in kinetic energy (∆KE):

∆KE = 23400 J - 3900 J

Now, we can find the final kinetic energy (KE_final) by adding the change in kinetic energy (∆KE) to the initial kinetic energy (KE_initial):

KE_final = KE_initial + ∆KE

Finally, we can calculate the final speed (v_final) using the formula for kinetic energy:

KE_final = (1/2) * m * v_final^2

Rearranging the equation, we have:

v_final^2 = (2 * KE_final) / m

Taking the square root of both sides, we find:

v_final = √((2 * KE_final) / m)

Substituting the values, we can find the final speed of the car.