A spacecraft of mass 3.5 x 102kg was moving at 1.5 x 102ms-1 when its motor, operating at 8.4 x 102 kW fired for 5.0s Find the new velocity acquired by the spacecraft

I don't know how to find the new velocity
i found the work
Power = w/t
840 x 5 = W
4200J = W

Dont know what to do next

(1/2) m Vnew^2 = (1/2) m Vold^2 + W

To find the new velocity acquired by the spacecraft, we can use the concept of work and energy.

First, calculate the work done by the motor using the formula:

Work = Power × time

Given:
Power = 8.4 × 10^2 kW = 8.4 × 10^5 W
Time = 5.0 s

Work = 8.4 × 10^5 W × 5.0 s
Work = 4.2 × 10^6 J (joules)

Now, since work is equal to the change in kinetic energy, we can say:

Work = ΔKE

Here, the spacecraft initially had a kinetic energy of:

KE_initial = (1/2) × mass × (initial velocity)^2
KE_initial = (1/2) × 3.5 × 10^2 kg × (1.5 × 10^2 m/s)^2

Next, we can find the final kinetic energy:

ΔKE = KE_final - KE_initial
ΔKE = (1/2) × mass × (final velocity)^2 - (1/2) × mass × (initial velocity)^2

Since the mass remains the same, we can rearrange the equation to solve for the final velocity:

(final velocity)^2 = 2 × (ΔKE / mass) + (initial velocity)^2
(final velocity)^2 = 2 × (4.2 × 10^6 J / 3.5 × 10^2 kg) + (1.5 × 10^2 m/s)^2

Solving the equation:

(final velocity)^2 = 2 × (1.2 × 10^4 m^2/s^2) + (2.25 × 10^4 m^2/s^2)
(final velocity)^2 = 2.4 × 10^4 m^2/s^2 + 2.25 × 10^4 m^2/s^2
(final velocity)^2 = 4.65 × 10^4 m^2/s^2

Taking the square root:

final velocity = √(4.65 × 10^4 m^2/s^2)
final velocity ≈ 215.44 m/s

Therefore, the new velocity acquired by the spacecraft is approximately 215.44 m/s.

To find the new velocity acquired by the spacecraft, you need to apply the concept of work and energy. First, find the work done using the power equation you have calculated correctly:

Work (W) = Power × time
W = 840 kW × 5 s
W = 4200 kJ (note: since power is given in kilowatts, the work will be in kilojoules)

Now, you need to make use of the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. Therefore, the work done by the spacecraft's motor will be equal to the change in its kinetic energy.

The initial kinetic energy of the spacecraft is given by:
Initial Kinetic Energy = 0.5 × mass × (initial velocity)^2

Substituting the given values:
Initial Kinetic Energy = 0.5 × (3.5 × 10^2 kg) × (1.5 × 10^2 m/s)^2

Next, find the final kinetic energy using:
Final Kinetic Energy = Initial Kinetic Energy + Work (from the motor)

Final Kinetic Energy = Initial Kinetic Energy + 4200 kJ

Finally, find the final velocity using:
Final Velocity = √((2 × Final Kinetic Energy) / mass)

Plug in the values you have and calculate the final velocity.