Question

The position of an object moving along a line is given by `p(t) = 2t - sin(( pi )/6t)`. What is the speed of the object at `t = 4`?

Answer 1

Speed at t = 4:
`v=2.26 m.s^(-1)`

Explanation:

If we are given position as a function of time, then the function for speed is the differential of that position function.

Differentiate p(t):
• Differential of `asin(bt) = abcos(bt)`
`v(t)=(dp(t))/(dt) = 2 - π/6cos(π/6t)`

Now substitute in the value of t to find the value of speed at that time (t = 4):
`v(4) = 2 - π/6cos(π/6× 4) = 2.26 m.s^(-1)`