A 2.00 kg toy car is moving to the right with a speed of 0.700 m/s without friction. If it experiences an impulse of -4.00 Ns, what is the object's speed and direction after the impulse occurs? 2.70 m/s to the right 5.40 m/s to the left 2.60 m/s to the right 1.30 m/s to the left
Question
A 2.00 kg toy car is moving to the right with a speed of 0.700 m/s without friction. If it experiences an impulse of -4.00 Ns, what is the object's speed and direction after the impulse occurs? 2.70 m/s to the right 5.40 m/s to the left 2.60 m/s to the right 1.30 m/s to the left
Solution
To solve this problem, we need to use the concept of impulse and momentum. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it.
Step 1: Calculate the initial momentum of the toy car. Momentum (p) is the product of mass (m) and velocity (v). So, p_initial = m * v = 2.00 kg * 0.700 m/s = 1.40 kg*m/s.
Step 2: Calculate the final momentum of the toy car. The impulse (J) is equal to the change in momentum (∆p). So, ∆p = J = -4.00 Ns. Since ∆p = p_final - p_initial, we can solve for p_final: p_final = ∆p + p_initial = -4.00 Ns + 1.40 kgm/s = -2.60 kgm/s.
Step 3: Calculate the final velocity of the toy car. Velocity is momentum divided by mass. So, v_final = p_final / m = -2.60 kg*m/s / 2.00 kg = -1.30 m/s.
The negative sign indicates that the direction of the velocity (and thus the movement of the toy car) has reversed. So, the toy car is moving to the left at a speed of 1.30 m/s after the impulse occurs. Therefore, the correct answer is "1.30 m/s to the left".
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