What is the average speed of an object that is still at t=0 and accelerates at a rate of a(t) =t/6 from t in [0, 1]?

1 Answer
Jan 4, 2016

You also need the initial speed of the object u_0. The the answer is:

u_(av)=0.042+u_0

Explanation:

Definition of acceleration:

a(t)=(du)/dt

a(t)*dt=du

int_0^ta(t)dt=int_(u_0)^udu

int_0^t(t/6)dt=int_(u_0)^udu

1/6int_0^t(t)dt=int_(u_0)^udu

1/6(t^2/2-0^2/2)=u-u_0

u(t)=t^2/12+u_0

To find the average speed:

u(0)=0^2/12+u_0=u_0

u(1)=1^2/12+u_0=1/12-u_0

u_(av)=(u_0+u_1)/2

u_(av)=(u_0+1/12+u_0)/2

u_(av)=(2u_o+1/12)/2

u_(av)=(2u_0)/2+(1/12)/2

u_(av)=u_0+1/24

u_(av)=0.042+u_0