A motorist traveling at 30 m/s passes a parked police car. At the instant the motorist passes the police car, the police car starts chasing the motorist with an acceleration of 3 m/s^2.
How far does the police car have to travel to catch the motorist?
20
How do u solve the question?
To find out how far the police car has to travel to catch the motorist, we need to determine the time it takes for the police car to catch up.
We can start by using the equation of motion for the motorist:
distance = initial velocity × time + 0.5 × acceleration × time^2
Since the motorist is traveling at a constant velocity of 30 m/s, their acceleration is 0. Therefore, the equation simplifies to:
distance = initial velocity × time
Now let's find the time it takes for the police car to catch up. The police car starts with an initial velocity of 0 and accelerates at 3 m/s^2. We can use the equation:
final velocity = initial velocity + acceleration × time
30 m/s (for the motorist) = 0 m/s (for the police car) + 3 m/s^2 × time
Solving for time:
time = (30 m/s) / (3 m/s^2)
time = 10 s
Now, we can substitute the time into the equation for distance, using the initial velocity of the motorist (30 m/s):
distance = (30 m/s) × (10 s)
distance = 300 m
Therefore, the police car has to travel 300 meters to catch the motorist.
The car is caught when
(3/2)*t^2 = 30 t.
Solve for the nonzero t and use that to compute the distance travelled.
I won't be helping you with the other questions because you are not showing any work or thought.