Question

1. k13q1

points: 1/4
a car coasts into a hill at 14.0 m/s. it slows down with a uniform acceleration of -1.0 m/s/s.
a. what is the cars speed after 7.0 s?
speed 7 m/s
info attempts:1/∞ submit
b. what is the cars displacement after 7.0 s?
displacement m
info attempts:2/∞ submit
c. what is the cars speed after 9.0 s?
speed m/s
info attempts:0/∞ submit
d. what is the cars displacement after 9.0 s?
displacement m
info attempts:0/∞ submit
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Explanation:

Step1: List given values

Initial speed $v_0 = 14.0\ \text{m/s}$, acceleration $a = -1.0\ \text{m/s}^2$

Step2: Solve (a): Speed at 7.0 s

Use $v = v_0 + at$
$v = 14.0 + (-1.0)(7.0) = 7.0\ \text{m/s}$

Step3: Solve (b): Displacement at 7.0 s

Use $x = v_0t + \frac{1}{2}at^2$
$x = (14.0)(7.0) + \frac{1}{2}(-1.0)(7.0)^2 = 98 - 24.5 = 73.5\ \text{m}$

Step4: Solve (c): Speed at 9.0 s

Use $v = v_0 + at$
$v = 14.0 + (-1.0)(9.0) = 5.0\ \text{m/s}$

Step5: Solve (d): Displacement at 9.0 s

Use $x = v_0t + \frac{1}{2}at^2$
$x = (14.0)(9.0) + \frac{1}{2}(-1.0)(9.0)^2 = 126 - 40.5 = 85.5\ \text{m}$

Answer:

a. $7.0\ \text{m/s}$
b. $73.5\ \text{m}$
c. $5.0\ \text{m/s}$
d. $85.5\ \text{m}$