A car of mass 1000kg is travelling along a straight flat road at a constant speed of 30.0ms^-1. It then accelerates with constant acceleration of 3.00ms^-2 for 10.0s, after which it continues to travels at a constant speed. Determine:
(a) The final speed of the car
(b) The distance did the car travelled during the acceleration
(c) The overall force acting on the car during the acceleration
(d) The initial momentum of the car
(e) The initial kinetic energy of the car
I understand its too do with the basic laws but I don't know which equations they are
To solve this problem, we will need to apply the basic laws of motion, such as Newton's second law and the equations of motion.
(a) To find the final speed of the car, we can use the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken. In this case, the initial velocity (u) is 30.0 m/s, the acceleration (a) is 3.00 m/s^2, and the time (t) is 10.0 s. Plugging these values into the equation, we get:
v = 30.0 m/s + (3.00 m/s^2)(10.0 s)
v = 30.0 m/s + 30.0 m/s
v = 60.0 m/s
Therefore, the final speed of the car is 60.0 m/s.
(b) To find the distance traveled by the car during the acceleration phase, we can use the equation of motion:
s = ut + (1/2)at^2
where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time taken. In this case, the initial velocity (u) is 30.0 m/s, the acceleration (a) is 3.00 m/s^2, and the time (t) is 10.0 s. Plugging these values into the equation, we get:
s = (30.0 m/s)(10.0 s) + (1/2)(3.00 m/s^2)(10.0 s)^2
s = 300 m + (1/2)(3.00 m/s^2)(100.0 s^2)
s = 300 m + 150 m
s = 450 m
Therefore, the car travels a distance of 450 meters during the acceleration phase.
(c) To determine the overall force acting on the car during the acceleration, we can use Newton's second law:
F = ma
where F is the force, m is the mass of the car, and a is the acceleration. In this case, the mass (m) of the car is 1000 kg, and the acceleration (a) is 3.00 m/s^2. Plugging these values into the equation, we get:
F = (1000 kg)(3.00 m/s^2)
F = 3000 N
Therefore, the overall force acting on the car during the acceleration phase is 3000 Newtons.
(d) To find the initial momentum of the car, we need to use the equation:
p = mv
where p is the momentum of the car, m is the mass of the car, and v is the initial velocity. In this case, the mass (m) of the car is 1000 kg, and the initial velocity (v) is 30.0 m/s. Plugging these values into the equation, we get:
p = (1000 kg)(30.0 m/s)
p = 30000 kg·m/s
Therefore, the initial momentum of the car is 30000 kilogram meters per second.
(e) To calculate the initial kinetic energy of the car, we can use the equation:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass of the car, and v is the initial velocity. In this case, the mass (m) of the car is 1000 kg, and the initial velocity (v) is 30.0 m/s. Plugging these values into the equation, we get:
KE = (1/2)(1000 kg)(30.0 m/s)^2
KE = (1/2)(1000 kg)(900 m^2/s^2)
KE = 450000 J
Therefore, the initial kinetic energy of the car is 450000 Joules.