Question:

A toy car with a mass of 0.5 kg is initially at rest. It is then pushed with a constant force of 2 N for 0.4 seconds in the positive x-direction. The car moves 0.5 meters during this time.

a) Calculate the final velocity of the car. b) Calculate the change in momentum of the car. c) Is linear momentum conserved in this scenario? Explain your answer.

Answer:

a) To calculate the final velocity of the car, we can use the equation:

where $v_f$ is the final velocity, $v_i$ is the initial velocity (which is 0 in this case, since the car is initially at rest), $a$ is the acceleration, and $t$ is the time.

Since the acceleration is given by the equation:

where $F$ is the force applied to the car, and $m$ is the mass of the car.

Plugging in the given values, we have:

$F = 2 \, \text{N}$ $m = 0.5 \, \text{kg}$ $t = 0.4 \, \text{s}$

Plugging the values of $v_i$, $a$, and $t$ into the equation for final velocity, we get:

Therefore, the final velocity of the car is $1.6 \, \text{m/s}$.

b) The change in momentum of an object is given by the equation:

where $\Delta p$ is the change in momentum, $p_f$ is the final momentum, and $p_i$ is the initial momentum.

The momentum of an object is given by the equation:

where $m$ is the mass of the object, and $v$ is the velocity of the object.

Since the initial velocity of the car is 0, the initial momentum is 0.

Plugging the values of $m$ and $v_f$ into the equation for final momentum, we get:

Therefore, the change in momentum of the car is $0.8 \, \text{kg} \cdot \text{m/s}$.

c) Linear momentum is conserved in this scenario. According to the principle of conservation of linear momentum, the total momentum of an isolated system remains constant if no external forces are acting on it. In this case, the car is the only object involved, and there are no external forces acting on it apart from the applied force. Since we considered the system to be isolated, the force exerted on the car does not contribute to any change in momentum of other objects. Therefore, we can conclude that linear momentum is conserved in this scenario.