A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance d ( t ) ( in ft ) that the car travels t seconds after the brakes are applied is given by d ( t ) = − 4.84 t 2 + 88 t , where 0 ≤ t ≤ 9.09 . ( See Example 5 ) a. Find the difference quotient d ( t + h ) − d ( t ) h . Use the difference quotient to determine the average rate of speed on the following intervals for t . b. [ 0 , 2 ] ( Hint : t = 0 and h = 2 ) c. [ 2 , 4 ] ( Hint : t = 2 and h = 2 ) d. [ 4 , 6 ] ( Hint : t = 4 and h = 2 ) e. [ 6 , 8 ] ( Hint : t = 6 and h = 2 )
A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance d ( t ) ( in ft ) that the car travels t seconds after the brakes are applied is given by d ( t ) = − 4.84 t 2 + 88 t , where 0 ≤ t ≤ 9.09 . ( See Example 5 ) a. Find the difference quotient d ( t + h ) − d ( t ) h . Use the difference quotient to determine the average rate of speed on the following intervals for t . b. [ 0 , 2 ] ( Hint : t = 0 and h = 2 ) c. [ 2 , 4 ] ( Hint : t = 2 and h = 2 ) d. [ 4 , 6 ] ( Hint : t = 4 and h = 2 ) e. [ 6 , 8 ] ( Hint : t = 6 and h = 2 )
Solution Summary: The author calculates the difference quotient of the distance function d(t)=-4.84t
A car traveling 60 mph (88 ft/sec) undergoes a constant deceleration until it comes to rest approximately 9.09 sec later. The distance
d
(
t
)
(
in ft
)
that the car travels t seconds after the brakes are applied is given by
d
(
t
)
=
−
4.84
t
2
+
88
t
, where
0
≤
t
≤
9.09
. (See Example 5 )
a. Find the difference quotient
d
(
t
+
h
)
−
d
(
t
)
h
.
Use the difference quotient to determine the average rate of speed on the following intervals for t.
Solve questions by Course Name (Ordinary Differential Equations II 2)
please Solve questions by Course Name( Ordinary Differential Equations II 2)
InThe Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth.
Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth
from which the flash is visible? (Earth’s radius is approximately 4000 miles.)
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