Question

An object is traveling along the x axis so that its speed is given by v(t)=t^2-7t+10 m/s.

(a) Find the times when the object is at rest.
(b) Find the acceleration at both of these times. Interpret the acceleration in
terms of the motion of the object, ie whether the object is increasing or
decreasing in speed and in which direction.
(c) If the object is at x=-1 m at t=1, find the position of the object at time t.
(d) Find the leftmost position of the object for all t 0.

Answer 1

a)
when is v = 0?
(t-5)(t-2) = 0
t = 5 or 2

b)
a = 2 t - 7
put in t = 5 and t = 2


c)
x = (1/3) t^3 - (7/2) t^2 + 10 t + c
put in given point to find c

d)
when is x a minimum?
When v = 0
so put in t = 5 and t = 2 and find the lower x value