To calculate the force needed to accelerate a 1000-kg car at a rate of 3 m/s², we can use Newton's second law of motion, which states that force (F) equals mass (m) multiplied by acceleration (a). Given that the mass of the car is 1000 kg and the acceleration is 3 m/s², we can calculate the force using the formula:
Force (F) = mass (m) * acceleration (a)
Plugging in the values:
F = 1000 kg * 3 m/s²
F = 3000 kg·m/s² or 3000 N
Therefore, the force needed to accelerate the 1000-kg car at a rate of 3 m/s² is 3000 N.
2. To find the acceleration of a 70-kg swimmer who pushes off a pool wall with a force of 250 N, we can rearrange Newton's second law of motion formula to solve for acceleration (a). Given that the force is 250 N and the mass is 70 kg, we can use the formula:
Force (F) = mass (m) * acceleration (a)
Rearranging the formula to solve for acceleration:
a = F / m
Plugging in the values:
a = 250 N / 70 kg
a ≈ 3.57 m/s²
Therefore, the acceleration of the swimmer is approximately 3.57 m/s².
3. To determine the mass of a football player who experiences a force of 1250 N and has an acceleration of 1.5 m/s², we can rearrange the formula F = m * a. Given that the force is 1250 N and the acceleration is 1.5 m/s², we can use the formula:
Force (F) = mass (m) * acceleration (a)
Rearranging the formula to solve for mass:
m = F / a
Plugging in the values:
m = 1250 N / 1.5 m/s²
m ≈ 833.33 kg
Therefore, the mass of the football player is approximately 833.33 kg.
4. To calculate the acceleration given a 45 kg child with a 0.75 N push on a swing, we can rearrange the formula F = m * a. Given that the force is 0.75 N and the mass is 45 kg, we can use the formula:
Force (F) = mass (m) * acceleration (a)
Rearranging the formula to solve for acceleration:
a = F / m
Plugging in the values:
a = 0.75 N / 45 kg
a ≈ 0.017 m/s²
Therefore, the acceleration given to the 45 kg child with a 0.75 N push on a swing is approximately 0.017 m/s².
5. To find the mass of a car that is accelerating at 2 m/s² and then hits a tree with a force of 6000 N, we can rearrange the formula F = m * a. Given that the force is 6000 N and the acceleration is 2 m/s², we can use the formula:
Force (F) = mass (m) * acceleration (a)
Rearranging the formula to solve for mass:
m = F / a
Plugging in the values:
m = 6000 N / 2 m/s²
m = 3000 kg
Therefore, the mass of the car that is accelerating at 2 m/s² and then hits a tree with a force of 6000 N is 3000 kg.