Question

1. what is the magnitude of the net force acting on a $2.0 \times10^3$ kilogram car as it accelerates from rest to a speed of 15 meters per second in 5.0 seconds?

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1. a 5.00 kilogram mass is traveling at 100 meters per second. calculate the speed of the mass after an impulse of 30 newton*seconds is applied in the direction of its motion.

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1. a bullet traveling at $5.0 \times10^2$ meters per is brought to rest by an impulse of 50 newton*seconds. find the mass of the bullet.

Explanation:

(Problem 4):

Step1: Calculate acceleration

$a = \frac{v_f - v_i}{t} = \frac{15\ \text{m/s} - 0}{5.0\ \text{s}} = 3.0\ \text{m/s}^2$

Step2: Calculate net force

$F_{net} = m \cdot a = (2.0 \times 10^3\ \text{kg}) \cdot (3.0\ \text{m/s}^2)$

(Problem 5):

Step1: Relate impulse to velocity change

$J = m \cdot \Delta v \implies \Delta v = \frac{J}{m} = \frac{30\ \text{N·s}}{5.00\ \text{kg}} = 6.00\ \text{m/s}$

Step2: Find final speed

$v_f = v_i + \Delta v = 100\ \text{m/s} + 6.00\ \text{m/s}$

(Problem 6):

Step1: Relate impulse to mass

$J = m \cdot |v_f - v_i| \implies m = \frac{J}{|v_f - v_i|} = \frac{50\ \text{N·s}}{|0 - 5.0 \times 10^2\ \text{m/s}|}$

Step2: Compute mass value

$m = \frac{50\ \text{N·s}}{500\ \text{m/s}}$

Answer:

1. Problem 4: $6.0 \times 10^3\ \text{Newtons}$
2. Problem 5: $106\ \text{meters per second}$
3. Problem 6: $0.10\ \text{kilograms}$