# Worksheet: Using Integration to Find Power

In this worksheet, we will practice using integration to solve problems involving power as a function of time to find work, speed, or time.

**Q1: **

A car has mass 1β066 kg. At time seconds, its engine works at a rate of . Given that at the carβs speed is 78 km/h , find its speed at . Give your answer to the nearest m/s.

**Q3: **

The power of a machine is given by the relation , where is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

**Q4: **

The power of an engine is given by hp, where is the time in seconds. Find the power of the engine when , the work done over the time interval , and the maximum power of the engine.

- A , ,
- B , ,
- C , ,
- D , ,

**Q5: **

The power of an engine at time seconds is given by . Find the work done by the engine between and .

**Q8: **

The power of a machine is given by the relation , where is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

**Q9: **

The power of a machine is given by the relation , where is the time elapsed in seconds. Find the work done by the machine in the first 6 seconds.

**Q10: **

The power of an engine is given by hp, where is the time in seconds. Find the power of the engine when , the work done over the time interval , and the maximum power of the engine.

- A , ,
- B , ,
- C , ,
- D , ,

**Q11: **

The power of an engine is given by hp, where is the time in seconds. Find the power of the engine when , the work done over the time interval , and the maximum power of the engine.

- A , ,
- B , ,
- C , ,
- D , ,

**Q12: **

A car has mass 951 kg. At time seconds, its engine works at a rate of . Given that at the carβs speed is 73 km/h , find its speed at . Give your answer to the nearest m/s.