SOLUTION: can someone show me how to do this problem: Suppose that the speed (in m/sec) of a particle moving on the x-axis at time t seconds (t is greater than or equal to 0) is given by:

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Question 163209: can someone show me how to do this problem:
Suppose that the speed (in m/sec) of a particle moving on the x-axis at time t seconds (t is greater than or equal to 0) is given by:
V(t) = t^3 - 8t^2 + 15t + 10.
By sketching a graph of V(t), estimate during what time period the speed of the particle is less than 10m/sec.
a. Between about t = 2 and t = 4 seconds
b. Between about t = 4 and t = 6 seconds
c. Between about t = 4 and t = 5 seconds
d. Between about t = 3 and t = 5 seconds
Answer by Edwin McCravy(20086) (Show Source):
You can put this solution on YOUR website!
can someone show me how to do this problem:
Suppose that the speed (in m/sec) of a particle moving
on the x-axis at time t seconds (t is greater than or equal to 0)
is given by:
V(t) = t^3 - 8t^2 + 15t + 10.
By sketching a graph of V(t), estimate during what time period the speed of the particle is less than 10m/sec.
a. Between about t = 2 and t = 4 seconds
b. Between about t = 4 and t = 6 seconds
c. Between about t = 4 and t = 5 seconds
d. Between about t = 3 and t = 5 seconds

now draw a green horizontal line through 10 on the t-axis
(shown as the x-0axis):

Draw a black vertical line where the curve starts dropping
below the green line, and another one at the end of the
place where it drops below the green line.

Notice that the vertical lines crosses the t-axis (actually
here it's the x-axis) at 3 and 5:
Answer: The speed is below 10 m/sec when t is between 3 and 5
seconds.
Edwin