A motorist driving a 1100-kg car on level ground accelerates from 20.0 m/s to 30.0 m/s in a time of 5.6 s. Neglecting friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.
To determine the average mechanical power supplied by the engine during this time interval, we first need to calculate the net force acting on the car.
The net force can be found using Newton's second law of motion, which states that the net force is equal to the mass of the object multiplied by its acceleration:
F_net = m * a
In this case, the mass of the car is given as 1100 kg, and the acceleration can be calculated using the equation for average acceleration:
a = (v_f - v_i) / t
where v_f is the final velocity (30.0 m/s), v_i is the initial velocity (20.0 m/s), and t is the time interval (5.6 s).
Let's calculate the acceleration first:
a = (30.0 m/s - 20.0 m/s) / 5.6 s
a = 1.79 m/s^2
Now we can calculate the net force:
F_net = 1100 kg * 1.79 m/s^2
F_net = 1969 N
The power supplied by the engine can be found using the equation for mechanical power:
P = F_net * v
where F_net is the net force and v is the velocity.
Since the velocity is changing throughout the time interval, we can take the average velocity as the average of the initial and final velocities:
v_avg = (v_f + v_i) / 2
v_avg = (30.0 m/s + 20.0 m/s) / 2
v_avg = 25.0 m/s
Now we can calculate the average mechanical power:
P = F_net * v_avg
P = 1969 N * 25.0 m/s
P = 49225 W (or 49.2 kW)
Therefore, the average mechanical power the engine must supply during this time interval is approximately 49.2 kW.