You solve #1 and #3 by applying Newton's Second Law, F = m a.
For the second problem, you first need to solve for the required deceleration rate. a = F/m = 5 m/s^2
The time it takes to stop is
t = Vo/a = (30 m/s)/5 m/s^2 = 6 s
The distance travelled while stopping is that stopping time multiplied by the average velocity (Vo/2),
15 m/s * 6 s = 90 m
From Newtons' 2nd Law of Motion,
F = ma
F = braking force = 10,000 N
m = mass of the car = 2,000 kg.
a = acceleration
-10,000 = 2,000(a)
NOTE the negative sign attached to the braking force. This simply denotes that the direction of this particular force is opposite that of the motion of the automobile.
Solving for "a",
a = -10,000/2,000
a = -5 m/sec^2
The negative value of the acceleration means that when the brakes were applied, the car, obviously, was slowing down until it came to a complete stop.
The next formula to use is
Vf^2 - Vo^2 = 2as
Vf = final velocity = 0 (when the car finally stops)
Vo = initial velocity = 30 m/sec (given)
a = acceleration = -5 m/sec^2 (as calculated above)
s = stopping distance of car
0 - 30^2 = 2(-5)(s)
-900 = -10s
and solving for "s",
s = 900/10
s = 90 meters
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