Question

The position of an object moving along a line is given by `p(t) = 4t - sin(( pi )/4t)`. What is the speed of the object at `t = 1`?

Answer 1

`4-pi/(4sqrt2)`

Explanation:

Position of an object `p(t)=4t-sin(pi/4t)`

Speed is defined as the rate of change in position of object with respect to time.
To find the speed we need to differentiate `p(t)` with respect to `t`.
speed `=d/dt(p(t))`
`v=d/dt(p(t))=d/dt(4t-sin(pi/4t))`
`v=4-(pi/4)cos(pi/4t)`

At time `t=1`
`v_(t=1)=4-(pi/4)cos(pi/4(1))=4-pi/4(1/sqrt2)=4-pi/(4sqrt2)`