A car of mass 400kg starts from rest and attains a velocity of 30m/s in 5s
(i) find its acceleration
(ii)calculate the resultant force
(iii) How far did the car travel in 5s
(i) To find the acceleration, we can use the equation:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity is zero and the final velocity is 30 m/s, and the time is 5 seconds, we can plug these values into the equation:
acceleration = (30 m/s - 0 m/s) / 5 s = 6 m/s^2
So, the acceleration of the car is 6 m/s^2.
(ii) To calculate the resultant force, we can use Newton's second law of motion, which states that force equals mass times acceleration:
force = mass * acceleration
Given that the mass of the car is 400 kg and the acceleration is 6 m/s^2, we can plug in these values:
force = 400 kg * 6 m/s^2 = 2400 N
So, the resultant force acting on the car is 2400 N.
(iii) To find how far the car traveled in 5 seconds, we can use the equation for distance traveled during constant acceleration:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Given that the initial velocity is 0 m/s, the time is 5 seconds, and the acceleration is 6 m/s^2, we can plug these values into the equation:
distance = (0 m/s * 5 s) + (0.5 * 6 m/s^2 * (5 s)^2) = 0 + 75 m
So, the car traveled a distance of 75 meters in 5 seconds.
(i) To find the acceleration, we can use the equation:
acceleration = (final velocity - initial velocity) / time
Given that the initial velocity is 0 m/s, the final velocity is 30 m/s, and the time taken is 5 s, we can substitute these values into the equation:
acceleration = (30 m/s - 0 m/s) / 5 s
acceleration = 30 m/s / 5 s
acceleration = 6 m/s²
So, the acceleration of the car is 6 m/s².
(ii) To calculate the resultant force, we can use Newton's second law of motion:
force = mass × acceleration
Given that the mass of the car is 400 kg and the acceleration is 6 m/s², we can substitute these values into the equation:
force = 400 kg × 6 m/s²
force = 2400 N
So, the resultant force on the car is 2400 N.
(iii) To find how far the car traveled in 5 seconds, we can use the equation:
distance = initial velocity × time + 0.5 × acceleration × time²
Given that the initial velocity is 0 m/s, the time taken is 5 s, and the acceleration is 6 m/s², we can substitute these values into the equation:
distance = 0 m/s × 5 s + 0.5 × 6 m/s² × (5 s)²
distance = 0 m + 0.5 × 6 m/s² × 25 s²
distance = 0 m + 0.5 × 6 m/s² × 625 s²
distance ≈ 937.5 m
So, the car traveled approximately 937.5 meters in 5 seconds.