A driver of a car traveling at 14.2 m/s applies
the brakes, causing a uniform deceleration of
2.0 m/s
2
.
How long does it take the car to accelerate
to a final speed of 10.7 m/s?
Answer in units of s.
002 (part 2 of 2) 10.0 points
b) How far has the car moved during the
braking period?
Answer in units of m.
1425m
To find the time it takes for the car to accelerate to a final speed, we can use the equation of motion:
V = U + at
Here,
V = Final speed = 10.7 m/s
U = Initial speed = 14.2 m/s
a = Acceleration = -2.0 m/s^2 (negative because it is deceleration)
t = Time taken
Rearranging the equation, we get:
t = (V - U) / a
Substituting the given values:
t = (10.7 - 14.2) / -2.0
Calculating the result:
t = -3.5 / -2.0 = 1.75 seconds
Therefore, it takes the car 1.75 seconds to accelerate to a final speed of 10.7 m/s.
To find the distance the car has moved during the braking period, we can use the equation:
S = Ut + 0.5at^2
Here,
S = Distance moved
U = Initial speed = 14.2 m/s
t = Time taken = 1.75 seconds
a = Acceleration = -2.0 m/s^2
Substituting the values:
S = (14.2 * 1.75) + 0.5 * (-2.0) * (1.75)^2
Calculating the result:
S = 24.85 - 3.0625 = 21.7875 meters
Therefore, the car has moved approximately 21.79 meters during the braking period.