Question

An object moves along the x axis according to the equation x = 3, 15t2-2.00t + 3.00, where x is in meters and t is in seconds. (a) Determine the average speed between t-2.40 s and t 4.40 s m/s (b) Determine the instantaneous speed at t2.40 s m/s Determine the instantaneous speed at t4.40 s m/s (c) Determine the average acceleration between t-2.40 s and t- 4.40 s. m/s2 (d) Determine the instantaneous acceleration at t2.40 s m/s2 Determine the instantaneous acceleration at t 4.40 s. m/s2 (e) At what time is the object at rest?

Answer 1

Given is:-

The equation  

at t=2.40s the position of the object is

which gives

similarly at t=4.40s the position is  

which is  

thus the average speed is given by

by plugging all the values we get

Part-b

thus differentiating the given function w.r.t time we get

now

at=2.40 the instanteous velocity will be

similarlly

Part-c

which gives us

Part-d

By differentiating the velocity funtion w.r.t time we get

thus at time t=2.40 and at t=4.40 the instantaneous acceleration will be same

therefore

part-e

Object will be at rest when the velocity is zero therefore

which gives us