The position of an object moving along a line is given by p(t) = t-cos(( pi )/2t) . What is the speed of the object at t = 3 ?

1 Answer
Morgan
Dec 18, 2016

|v(t)|=|1-pi/2| ≈ 0.57 (units)

Explanation:

Speed is a scalar quantity having only magnitude (no direction). It refers to how fast an object is moving. On the other hand, velocity is a vector quantity, having both magnitude and direction. Velocity describes the rate of change of position of an object. For example, 40m/s is a speed, but 40m/s west is a velocity.

Velocity is the first derivative of position, so we can take the derivative of the given position function and plug in t=3 to find the velocity. The speed will then be the magnitude of the velocity.

p(t)=t-cos(pi/2t)

p'(t)=v(t)=1+pi/2sin(pi/2t)

The velocity at t=3 is calculated as

v(3)=1+pi/2sin((3pi)/2)

v(3)=1-pi/2

And then the speed is simply the magnitude of this result, such as that speed= |v(t)|

|v(t)|=|1-pi/2| ≈ 0.57 (units)

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