# 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 1β066 kg. At time seconds, its engine works at a rate of . Given that at the carβs speed is 78 km/h , find its speed at . Give your answer to the nearest m/s.

Q2:

Find the time taken for a car of 1β236 kg to reach a speed of 126 km/h, given that the car started from rest and that the power of the engine is constant and equal to 103 horsepowers.

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 .

Q6:

Find the time taken for a car of 1β188 kg to reach a speed of 126 km/h, given that the car started from rest and that the power of the engine is constant and equal to 110 horsepowers.

Q7:

Find the time taken for a car of 972 kg to reach a speed of 126 km/h, given that the car started from rest and that the power of the engine is constant and equal to 90 horsepowers.

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 carβs speed is 73 km/h , find its speed at . Give your answer to the nearest m/s.