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

1 Answer
A08
Dec 7, 2016

1 + pi

Explanation:

Velocity is defined as
v(t) -= (dp(t))/dt

Therefore, in order to find speed we need to differentiate function p(t) with respect to time. Please remember that v and p are vector quantities and speed is a scalar.

(dp(t))/dt = d/dt(t - t sin(pi/3 t))
=>(dp(t))/dt = d/dtt - d/dt(t sin(pi/3 t))

For the second term will need to use the product rule and chain rule as well. We get

v(t) = 1 - [t xxd/dtsin(pi/3 t)+sin(pi/3 t) xxd/dt t]
=>v(t) = 1 - [t xxcos(pi/3 t)xxpi/3+sin(pi/3 t)]
=>v(t) = 1 - [pi/3t cos(pi/3 t)+sin(pi/3 t)]

Now speed at t=3 is v(3), therefore we have

v(3) = 1 - [pi/3xx3 cos(pi/3 xx3)+sin(pi/3 xx3)]
=>v(3) = 1 - [pi cos(pi)+sin(pi)]

Inserting values of sin and cos functions
v(3) = 1 - [pixx(-1) +0]
v(3) = 1 + pi

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