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In this lesson, we will learn how to use integration to solve problems involving power as a function of time to find work, speed, or time.

Q1:

Find the time taken for a car of 1β236 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.

Q2:

Find the time taken for a car of 1β188 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.

Q3:

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.

Q4:

The power of a machine is given by the relation π = 3 π‘ + 7 , where π‘ is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

Q5:

The power of a machine is given by the relation π = 8 π‘ β 2 , where π‘ is the time elapsed in seconds. Find the work done by the machine in the first 8 seconds.

Q6:

The power of a machine is given by the relation π = 7 π‘ + 3 , where π‘ is the time elapsed in seconds. Find the work done by the machine in the first 6 seconds.

Q7:

The power of an engine is given by οΌ 8 π‘ β 1 1 5 π‘ ο 2 hp, where π‘ β [ 0 , 1 0 3 ] is the time in seconds. Find the power of the engine π 1 when π‘ = 3 6 s e c o n d s , the work done π over the time interval [ 0 , 1 2 ] , and the maximum power π m a x of the engine.

Q8:

The power of an engine is given by οΌ 8 π‘ β 1 2 0 π‘ ο 2 hp, where π‘ β [ 0 , 1 1 0 ] is the time in seconds. Find the power of the engine π 1 when π‘ = 3 4 s e c o n d s , the work done π over the time interval [ 0 , 1 9 ] , and the maximum power π m a x of the engine.

Q9:

The power of an engine is given by οΌ 5 π‘ β 1 2 0 π‘ ο 2 hp, where π‘ β [ 0 , 1 0 2 ] is the time in seconds. Find the power of the engine π 1 when π‘ = 6 8 s e c o n d s , the work done π over the time interval [ 0 , 2 1 ] , and the maximum power π m a x of the engine.

Q10:

A car has mass 1β066 kg. At time π‘ seconds, its engine works at a rate of π = οΉ π‘ + 9 π‘ ο 2 W . Given that at π‘ = 6 s the carβs speed is 78 km/h , find its speed at π‘ = 1 0 s . Give your answer to the nearest m/s.

Q11:

A car has mass 951 kg. At time π‘ seconds, its engine works at a rate of π = οΉ 3 π‘ + 9 π‘ ο 2 W . Given that at π‘ = 6 s the carβs speed is 73 km/h , find its speed at π‘ = 1 0 s . Give your answer to the nearest m/s.

Q12:

A car has mass 1β239 kg. At time π‘ seconds, its engine works at a rate of π = οΉ 5 π‘ + 9 π‘ ο 2 W . Given that at π‘ = 7 s the carβs speed is 57 km/h , find its speed at π‘ = 8 s . Give your answer to the nearest m/s.

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