Home > Physics > Acceleration

What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = t/4+2# from #t in [0, 6]#?

Answer 1

Julia Aguilar

#v_a=7,5" " m/s#

#"1- Find displacement at interval (0,6)"# #"2-use the formula :"v_a=(Delta x)/(Delta t)#

#v(t)=int a(t) d t" ; "x=int_a^b v(t)d t#

#v(t)=int(t/4+2)d t=1/4*1/2 t^2+2t+C# #v(t)=1/8 t^2+2t+C" for t=0 ; v=0 ; C=0"# #v(t)=1/8t^2+2t#

Delta x is equal to int_0^6(1/8t^2+2t)d t.

#Delta x=|1/8*1/3*t^3+2*1/2*t^2|_0^6# #Delta x=(1/24*6^3+6^2)-(0+0)#

#Delta x=9+36# #Delta x=45#

#v_a=45/(6-0)# #v_a=45/6# #v_a=7,5" " m/s#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

William Audy

The average speed is 9 units per time interval.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.