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In this lesson, we will learn how to solve motion along a line and how to use differentiation to describe the motion along the line.

Q1:

A particle is moving in a straight line such that its displacement π after π‘ seconds is given by Determine the time interval during which the velocity of the particle is increasing.

Q2:

A particle moves in a straight line such that at time π‘ seconds its displacement from a fixed point on the line is given by Determine whether the particle is accelerating or decelerating when π‘ = 2 s .

Q3:

A particle started moving along the π₯ -axis. When the particleβs displacement from the origin is π₯ metres, its velocity is given by Find the particleβs acceleration when its velocity vanished.

Q4:

A particle moves along the π₯ -axis such that at time seconds ( π‘ β₯ 0 ) its velocity is given by π£ = ( 3 π‘ β 9 π‘ ) / 2 m s . Determine the time interval in which the particle decelerates.

Q5:

A particle is moving in a straight line such that its displacement after π‘ seconds is given by When the particleβs velocity is zero, its acceleration is π m/s^{2}. Find all the possible values of π .

Q6:

A particle moves along the π₯ -axis. At time π‘ seconds, its displacement from the origin is given by Determine the time at which the particleβs acceleration is 9 m/s^{2}.

Q7:

A particle is moving in a straight line such that its displacement π at π‘ seconds is given by Find the velocity of the particle when the acceleration is zero.

Q8:

A particle is moving in a straight line such that its displacement π in metres is given as a function of time π‘ in seconds by Find the magnitude of the acceleration of the particle when the velocity is zero.

Q9:

A particle moves along the π₯ -axis such that at time π‘ seconds, its displacement from the origin is given by What is the particleβs average velocity in the first 10 seconds?

Q10:

A particle is moving in a straight line such that its position π meters relative to the origin at time π‘ seconds is given by Find the particleβs average velocity between π‘ = 2 s and π‘ = 4 s .

Q11:

A particle moves along the π₯ -axis. When its displacement from the origin is π m, its velocity is given by Find the particleβs acceleration when π = 3 m .

Q12:

A particle started moving along the π₯ -axis. At time π‘ seconds, the its displacement from the origin is given by Find the bodyβs average speed within the time interval [ 0 , 5 ] .

Q13:

A body moves along the π₯ -axis such that at time π‘ seconds, its displacement from the origin is given by What is its velocity when its acceleration is equal to 0?

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