A motorist travels at a constant speed of 34.0 m/s through a school zone; exceeding the posted speed limit. A policeman, waits 7.0 s before giving chase at an acceleration of 3.9 m/s2.
(a) Find the time required to catch the car, from the instant the car passes the policeman.
2 s
(b) Find the distance required for the policeman to overtake the motorist.
3 m
Are 2s and 3 m your answers? Please show your work
I actually don't know where the 2s and 3m came from, I think it was a typo on my MSWord
(a) Measure time t from the instant the policeman passes the cop.
The speeder's distance travelled is
X1 = 34 t meters
The policeman's distance travelled (for t>7) is
X2 = (1/2)*3.9 (t-7)^2
Set X1=X2 and solve for t.
That is when the speeder is caught.
15.97
To find the time required for the policeman to catch the car, we need to determine the time it takes for the policeman to match the car's speed and then overtake it.
Given:
Initial speed of the car (v1) = 34.0 m/s
Police acceleration (a) = 3.9 m/s^2
Time delay before the policeman starts (t) = 7.0 s
(a) To find the time required, we can use the equation:
v2 = v1 + a * t
Where:
v2 - final velocity of the car when the policeman catches up
v1 - initial velocity of the car
a - acceleration of the policeman
t - time delay before the policeman starts
Substituting the given values:
v2 = 34.0 m/s + (3.9 m/s^2) * 7.0 s
v2 = 34.0 m/s + 27.3 m/s
v2 = 61.3 m/s
Now, to find the time required for the policeman to catch the car, we can use the equation:
t = (v2 - v1) / a
Substituting the values:
t = (61.3 m/s - 34.0 m/s) / 3.9 m/s^2
t = 27.3 m/s / 3.9 m/s^2
t ≈ 7 s
Therefore, it takes approximately 7 seconds for the policeman to catch the car from the instant the car passes the policeman.
(b) To find the distance required for the policeman to overtake the motorist, we can use the equation:
d = v1 * t + (1/2) * a * t^2
Substituting the values:
d = 34.0 m/s * 7 s + (1/2) * 3.9 m/s^2 * (7 s)^2
d = 238 m + 0.5 * 3.9 m/s^2 * 49 s^2
d = 238 m + 95.55 m
d ≈ 334 m
Therefore, the distance required for the policeman to overtake the motorist is approximately 334 meters.