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finding the time when the rate of change in speed=0 watch

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    in vector system,

    at t=2, a= -6i-2j and v= 3i-4j

    in order to calculate the rate at which the object's speed is changing,
    we were told to use a dot product.

    so a.v=|a||v|cos (x)

    since |a| cos (x) would give us the rate, we do the dot product of a and v to give -10, and divide this value by the magnitude of v which gives the value of acceleration to be -2 (which is correct according to the mark scheme).

    Then I was asked 'at what time is the rate of change of the object's speed equal to zero, and what is the speed at this instant?
    The answer is t=2.25s, v=4.73m/s

    Can anyone please explain to me how to approach the last question?

    Thanks in advance!
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    (Original post by liemluji)
    in vector system,

    at t=2, a= -6i-2j and v= 3i-4j

    in order to calculate the rate at which the object's speed is changing,
    we were told to use a dot product.

    so a.v=|a||v|cos (x)

    since |a| cos (x) would give us the rate, we do the dot product of a and v to give -10, and divide this value by the magnitude of v which gives the value of acceleration to be -2 (which is correct according to the mark scheme). ...
    A few things to note.

    The rate of change of speed is NOT the value of acceleration.

    The rate of change of speed is the component of the acceleration in the direction of the velocity.

     |\vec{a}| cos(\theta) is the component of the acceleration that is parallel to the direction of the velocity when you do the dot product of the acceleration and velocity vectors.

    (Original post by liemluji)
    ... Then I was asked 'at what time is the rate of change of the object's speed equal to zero, and what is the speed at this instant?
    The answer is t=2.25s, v=4.73m/s

    Can anyone please explain to me how to approach the last question?

    Thanks in advance!
    Are you given the velocity vector as a function of time? If yes, find the dot product of acceleration and velocity vectors and equate to zero to find the time.

    Or else you post the whole question.
 
 
 
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