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A car travelling at a constant speed of 30 m/s passes a police car at rest.
The policeman starts to move at the moment the speeder passes his car and
accelerates at a constant rate of 3.0 m/ s^{ 2} until he pulls even with the
speeding car. Find a) the time required for the policeman to catch the speeder
and b) the distance travelled during the chase.
Solution:
We are given, for the speeder:
v_{0}^{s} = 30 m/s | = | v^{ s} | |
a^{ s} = 0 |
v_{0}^{p} | = | ||
a^{ p} | = | 3.0 m/s ^{2}. |
30t = (3.0)t^{ 2}. |
x^{ s} = 30(20) = 600 m |
x^{ p} = (3.0)(20)^{2} = 600 m = x^{ s}. |
A car decelerates at
2.0 m/s ^{2} and comes to a stop after travelling
25 m.
Find a) the speed of the car at the start of the deceleration and b) the time
required to come to a stop.
Solution:
We are given:
a | = | - 2.0 m/s ^{2} | |
v | = | ||
x | = | 25 m |
A stone is thrown vertically upward from the edge of a building 19.6 m high
with initial velocity 14.7 m/s. The stone just misses the building on the way
down. Find a) the time of flight and b) the velocity of the stone just before
it hits the ground.
Solution:
We are given,
v_{0} | = | 14.7 m/s | |
a | = | - 9.8 m/s ^{2} |
x | = | - 19.6 m |
t | = | ||
= | |||
= | (- 14.7 24.5). |
A rocket moves upward, starting from rest with an acceleration
of
29.4 m/s ^{2} for 4 s. At this time, it runs out of fuel and
continues to
move upward. How high does it go?
Solution:
For the first stage of the flight we are given:
v_{0} | = | ||
a | = | 29.4 m/s ^{2} | |
t | = | 4 s |
For the second stage of the flight we start with,
v_{1} | = | 117.6 m/s | |
a | = | - 9.8 m/s ^{2} |
v_{2}^{2} - v_{1}^{2} | = | 2a(x_{2} - x_{1}) | |
(x_{2} - x_{1}) | = | (v_{2}^{2} - v^{ 2}_{1}) | |
= | (- (117.6)^{2}) | ||
= | 705.6 m. |
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