Physics energy questions

Question

1.A car has 29,321 J of energy when moving down the street. The mass of the vehicle is 1,619 kg. What velocity is the car  moving at?

2.A 1,368 N rocket travels at constant speed for 1,888 m in 2.6 seconds. What is the kinetic energy of the rocket? 

3.A bullet has 872 J of energy when traveling 211 m/s. What will the velocity of the bullet be when it has 169 J?

*answer and explanation please*

Answer 1

1. KE = .5*m*v² = 29321, you have mass so just plug in and solve for velocity.
2. V = distance / time = 1888 / 2.6 so KE = 0.5*m*(1888/2.6)² and plug in the mass that the problem gave you.
3. KE = .5*m*v² ... we need to find the bullet's mass so .5*m*(211)² = 872.... now you solve for mass and you can plug into the energy equation for 169 = .5*m*v² and this time you just solved for m so you plug that in and solve for v.

Explanation of work and kinetic energy:

Work = change in kinetic energy = F*d (applying a force over a distance adds energy, so basically adds velocity to the system, which makes sense because if u keep pushing something it'll get faster)

To get the formula you need a little calculus:

F = d(KE)/dx, F*dx = d(KE) = m*(dv/dt)*dx = m*v*dv and integrate to get .5*m*v²

Answer 2

1) When the car is moving, the energy responsible for the motion is kinetic energy, KE = 1/2mv² = 29321J

where m = 1619kg and v = velocity. Making v the subject and plugging in the given numbers yields

v = √(2*29321/1619) = 6.0m/s

2) Rewrite the constant speed as v = d/t = 1,888/2.6 = 726.15m/s

But the force, F = ma = mv/t = 1368N. Solving for the mass, m

==> m = Ft/v = 4.9kg and with this mass, you can find the kinetic energy of the rocket using

KE = 1/2mv² = 1/2(4.9kg)(726.15m/s)² = 1,291,869.9J

3) Again, the kinetic energy KE = 1/2mv² = 872J. Find the mass of the bullet

==> m = 2(872J)/(211m/s)² = 0.039kg. With this mass, you can find the new velocity of the bullet using the new given energy.

==> v = √(2*169J/0.039kg) = 92.9m/s