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In this lesson, we will learn how to use definite integrals to solve problems involving rectilinear motion.

Q1:

A car, starting from rest, began moving in a straight line from a fixed point. Its velocity after π‘ seconds is given by Calculate the displacement of the car when π‘ = 9 s e c o n d s .

Q2:

A particle accelerates at the rate of 2 π‘ + 7 m/s^{2} after π‘ seconds of motion. If π£ ( 0 ) = β 8 m/s, how long does it take for the velocity to reach 50 m/s? Give your answer to 2 decimal places.

Q3:

If π ( π‘ ) = πΉ ( π‘ ) β² is the velocity of a particle in motion, in kilometres per hour, what is the unit of οΈ π ( π‘ ) π‘ π π d ?

Q4:

A particle is moving in a straight line such that its acceleration at time π‘ seconds is given by Given that its initial velocity is 20 m/s, find an expression for its displacement in terms of π‘ .

Q5:

A particle moves along the π₯ -axis. At time π‘ seconds, its acceleration is given by Given that at π‘ = 2 s , its velocity is 28 m/s, what is its initial velocity?

Q6:

A particle is moving in a straight line such that its velocity at time π‘ seconds is given by Given that its initial position from a fixed point is 20 m, find an expression for its displacement at time π‘ seconds.

Q7:

A particle is moving in a straight line such that its velocity at time π‘ seconds is given by Given that its initial position from a fixed point is 4 m, find an expression for its displacement at time π‘ seconds.

Q8:

The figure shows a velocity-time graph for a particle moving in a straight line. Find the total distance the particle travelled.

Q9:

Q10:

A particle moves along the positive π₯ axis, starting at π₯ = 1 m . Itβs acceleration varies directly with π‘ 2 , where π‘ is the time in seconds. At π‘ = 1 s , the particleβs displacement is 12 m, and its velocity is 14 m/s. Express the particleβs displacement, π , and its velocity, π£ , in terms of π‘ .

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