Question

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`?

Answer 1

`|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)