A 2.31 × 103 kg car requires 4.2 kJ of work to move from rest to some final speed. During this time, the car moves 26.0 m. Neglecting friction, find a) the final speed. Answer in units of m/s
KE=1/2*m*v^2
solve for v
To find the final speed of the car, we can apply the work-energy principle. According to this principle, the work done on an object is equal to the change in its kinetic energy.
The work done on the car is given as 4.2 kJ (kilojoules). We can convert this to joules by multiplying by 1000 since 1 kJ = 1000 J.
4.2 kJ * 1000 J/1 kJ = 4200 J
The change in kinetic energy is equal to the final kinetic energy (K_final) minus the initial kinetic energy (K_initial). Since the car starts from rest, its initial kinetic energy is zero.
Therefore, the work done on the car (4200 J) is equal to the final kinetic energy.
Now, we can calculate the final speed (v_final) using the equation for kinetic energy:
K_final = (1/2) * m * v_final^2
where m is the mass of the car. In this case, m = 2.31 × 10^3 kg.
Hence, we have:
4200 J = (1/2) * (2.31 × 10^3 kg) * v_final^2
Simplifying the equation:
8400 J = (2.31 × 10^3 kg) * v_final^2
Dividing both sides by (2.31 × 10^3 kg):
v_final^2 = 8400 J / (2.31 × 10^3 kg)
v_final^2 = 3.6364 m^2/s^2
Taking the square root of both sides, we have:
v_final = √(3.6364 m^2/s^2)
v_final ≈ 1.91 m/s
Therefore, the final speed of the car is approximately 1.91 m/s.