What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) =t^2-4# from #t in [2, 3]#?

1 Answer
Jan 12, 2018

Answer:

4.58 #m/sec#

Explanation:

Acceleration of the object is given as,#a=4t^2-4#
So,velocity will be #(t^3)/3-4t# (by integrating)
Hence,displacement will be,
#S=(t^4)/12-(2t^2)# (by integrating)
Hence,displacement with in t=2 to t=3 will be -4.58 meter
Now here distance=displacement that has happened in between 2 sec and 3 sec
Hence average speed with in this duration=(total distance covered/total time)
I.e #(4.58/1)# #m/sec# or 4.58 #m/sec#