A vehicle of mass 600kg, moving at a speed of 30ms^-1 collides with a stationary vehicle of mass 900kg. The two vehicles lock together on impact.

Calculate:

1) The speed of the two vehicles immediately after the impact.

2) The force of the impact, if the duration of the collision is 0.15s.

3) The acceleration of each vehicle during the impact.

1. M1*V1 + M2*V2 = M1*V + M2*V.

600*30 + 900*0 = 600V * 900V,
18000 = 1500V, V = 12 m/s.

2. V = Vo + a*t.
12 = 30 + a*0.15, a = -120 m/s^2.

F = M*a = (M1+M2)*a = 1500 * (-120) = -180,000 N.
The negative sign means the force opposed the motion.

3. a = -120 m/s^2.

To solve this problem, we can use the principle of conservation of momentum and the equation for force.

1) The speed of the two vehicles immediately after the impact can be found using the principle of conservation of momentum. According to this principle, the total momentum before the impact is equal to the total momentum after the impact.

The initial momentum (p_initial) of the first vehicle is given by the product of its mass (m1) and its initial velocity (v1):
p1_initial = m1 * v1

Similarly, the initial momentum (p_initial) of the second vehicle is given by the product of its mass (m2) and its initial velocity (v2):
p2_initial = m2 * v2

Since the two vehicles lock together on impact, they move as a single unit after the collision. Let's denote the final velocity of the two vehicles as vf.

The total momentum before the impact is equal to the total momentum after the impact:
p1_initial + p2_initial = (m1 + m2) * vf

Substituting the given values:
p1_initial = 600 kg * 30 m/s = 18000 kg m/s
p2_initial = 900 kg * 0 m/s = 0 kg m/s

(18000 kg m/s) + (0 kg m/s) = (600 kg + 900 kg) * vf
18000 kg m/s = 1500 kg * vf
vf = 18000 kg m/s / 1500 kg
vf = 12 m/s

Therefore, the speed of the two vehicles immediately after the impact is 12 m/s.

2) The force of the impact can be calculated using Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (dp) with respect to time (dt):

F = dp / dt

Since the vehicles are initially moving and then come to rest after the collision, the change in momentum is equal to the initial momentum.

The change in momentum (dp) is given by:
dp = p_final - p_initial

Since the final momentum (p_final) is zero (since the vehicles come to rest), and the initial momentum (p_initial) is given by m1 * v1 (as calculated before), the change in momentum is:
dp = -p_initial

The duration of the collision is given as 0.15s (dt = 0.15s). Substituting the values into the force equation:
F = (-18000 kg m/s) / 0.15 s

F = -120000 N

Therefore, the force of the impact is 120000 N.

3) The acceleration of each vehicle during the impact can be calculated using Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):

F = m * a

Since the two vehicles are locked together on impact, they experience the same force (F) during the collision. Therefore, the acceleration (a) of each vehicle is:
a = F / m

For the first vehicle of mass 600 kg:
a1 = 120000 N / 600 kg
a1 = 200 m/s^2

For the second vehicle of mass 900 kg:
a2 = 120000 N / 900 kg
a2 = 133.33 m/s^2

Therefore, the acceleration of the first vehicle during the impact is 200 m/s^2 and the acceleration of the second vehicle is 133.33 m/s^2.

To calculate the speed of the two vehicles immediately after the impact, we need to consider the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

1) The momentum of an object is defined as the product of its mass and velocity (p = mv). Considering the first vehicle (V1) with a mass of 600 kg and a velocity of 30 m/s, and the second vehicle (V2) with a mass of 900 kg and a velocity of 0 m/s:

Initial momentum (before the collision) = (mass of V1 * velocity of V1) + (mass of V2 * velocity of V2)
= (600 kg * 30 m/s) + (900 kg * 0 m/s)
= 18000 kg·m/s + 0 kg·m/s
= 18000 kg·m/s

After the collision, the two vehicles lock together and move with a common velocity (v), as they have combined into one system. Let's assume this common velocity is "v" m/s.

Final momentum (after the collision) = (mass of V1 + mass of V2) * velocity of the combined system
= (600 kg + 900 kg) * v
= 1500 kg * v

According to the principle of conservation of momentum, the initial and final momentum should be equal:

Initial momentum = Final momentum
18000 kg·m/s = 1500 kg * v
v = 18000 kg·m/s / 1500 kg
v = 12 m/s

Thus, the speed of the two vehicles immediately after the impact is 12 m/s.

2) To calculate the force of the impact, we can use the concept of impulse. Impulse (J) is defined as the product of force and the time interval over which it acts (J = F * Δt). In this case, we know the duration of the collision (Δt = 0.15 s).

Using the equation, impulse = change in momentum, we can calculate the force:

Impulse = (Final momentum - Initial momentum)
Force * Δt = (Final momentum - Initial momentum)
Force = (Final momentum - Initial momentum) / Δt
= (1500 kg * 12 m/s - 18000 kg·m/s) / 0.15 s
= (18000 kg·m/s - 18000 kg·m/s) / 0.15 s
= 0 N

Therefore, the force of the impact is 0 Newtons since the vehicles lock together and there is no separation between them.

3) To calculate the acceleration of each vehicle during the impact, we can use the equation F = ma, where F represents the force and a represents the acceleration of each vehicle.

From the previous calculation, we determined that the force of the impact is 0 N. Since the mass of each vehicle remains constant, the acceleration of each vehicle during the impact would also be 0 m/s² (zero acceleration).