a 1500kg sports car accelerates from 0 to 30 m/s in 8 seconds. Whaat is the power of its engine?
30000
1500
To find the power of the engine, we need to use the formula:
Power (P) = Work (W) / Time (t)
First, we need to find the work done by the car. The work done (W) is given by:
Work (W) = Force (F) × Distance (d)
In this case, the force is the net force acting on the car, which can be found using Newton's second law:
Force (F) = Mass (m) × Acceleration (a)
Given that the mass of the sports car is 1500 kg and the car accelerates from 0 to 30 m/s in 8 seconds, we can calculate the acceleration:
Acceleration (a) = (Final Velocity - Initial Velocity) / Time
= (30 m/s - 0 m/s) / 8 s
= 3.75 m/s^2
Now, we can calculate the force:
Force (F) = Mass (m) × Acceleration (a)
= 1500 kg × 3.75 m/s^2
= 5625 N (Newtons)
Next, we need to find the distance (d) traveled by the car during the acceleration. This can be done using the kinematic equation:
Distance (d) = Initial Velocity (v) × Time (t) + 0.5 × Acceleration (a) × Time (t)^2
Since the car starts from rest, the initial velocity (v) is 0 m/s:
Distance (d) = 0 m/s × 8 s + 0.5 × 3.75 m/s^2 × (8 s)^2
= 0 + 0.5 × 3.75 m/s^2 × 64 s^2
= 120 m
Now we have all the values needed to calculate the work done:
Work (W) = Force (F) × Distance (d)
= 5625 N × 120 m
= 675,000 Joules
Finally, we can calculate the power by dividing the work done by the time:
Power (P) = Work (W) / Time (t)
= 675,000 J / 8 s
= 84,375 Watts
Therefore, the power of the sports car's engine is 84,375 Watts.