A car is traveling at a steady 90 km/h in a 50 km/h zone. A police motorcycle takes off at the instant the car passes it, accelerating at a steady 7.3 m/s/s.How much time elapses before the motorcycle is moving as fast as the car? How far is the motorcycle from the car when it reaches this speed?
90,000 m/3600 s = 25 m/s
v = a t
so
25 = 7.3 t
t = 3.42 seconds
distance car went = 25*3.42
distance cycle went = (25/2)* 3.42
(average speed is half max speed if a is constnt)
Well, let's calculate how much time it takes! First, we need to convert the speeds to the same unit. So, the car is traveling at 90,000 meters per hour, and the motorcycle is accelerating at 7.3 meters per second squared.
To find the time it takes for the motorcycle to reach the same speed as the car, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the formula to solve for time, t = (v - u) / a, we have:
t = (90,000 m/h - 0 m/h) / (7.3 m/s^2)
Now, the tricky part is converting the car's speed from meters per hour to meters per second because the motorcycle's acceleration is given in meters per second squared. To do that, we divide the car's speed by 3.6 m/s (since there are 3600 seconds in an hour):
t = (90,000 m/h ÷ 3.6 m/s - 0 m/h) / (7.3 m/s^2)
Simplifying:
t = (25,000 m/s - 0 m/s) / (7.3 m/s^2)
t ≈ 3424.66 seconds
So, it takes approximately 3424.66 seconds for the motorcycle to reach the same speed as the car.
Now, to find the distance the motorcycle has traveled, we can use the formula s = ut + (1/2)at^2. Since the initial velocity of the motorcycle is 0 m/s, the formula simplifies to s = (1/2)at^2:
s = (1/2)(7.3 m/s^2)(3424.66 s)^2
s ≈ 420,671,643.22 meters
Therefore, when the motorcycle reaches the same speed as the car, it is approximately 420,671,643.22 meters away from the car. That's quite a distance! Maybe the motorcycle officer should invest in a faster bike.
To determine how much time elapses before the motorcycle is moving as fast as the car, we can use the equation of motion:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time taken
Given:
Initial velocity of the motorcycle, um = 0 m/s (since it takes off from rest)
Final velocity of the motorcycle, vm = 90 km/h = (90 * 1000) / 3600 = 25 m/s
Acceleration of the motorcycle, am = 7.3 m/s^2
Substituting the values into the equation and solving for t:
vm = um + am * t
25 = 0 + 7.3 * t
25 = 7.3t
t = 25 / 7.3
t ≈ 3.42 seconds
Therefore, it takes approximately 3.42 seconds for the motorcycle to reach the same speed as the car.
To find the distance the motorcycle has traveled when it reaches this speed, we can use the equation of motion:
s = ut + (1/2)at^2
Where:
s = distance traveled
u = initial velocity
t = time taken
a = acceleration
Since we know the motorcycle starts from rest (u = 0 m/s), we can simplify the equation to:
s = (1/2)at^2
Substituting the values:
s = (1/2) * 7.3 * (3.42^2)
s ≈ 35.85 meters
Therefore, the motorcycle is approximately 35.85 meters away from the car when it reaches the same speed.
To find the time it takes for the motorcycle to reach the same speed as the car, we can use the kinematic equation:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
The car is traveling at a speed of 90 km/h = 90,000 m/3600 s = 25 m/s.
The motorcycle is initially at rest, so its initial velocity (u) is 0 m/s.
The acceleration of the motorcycle (a) is 7.3 m/s^2.
Substituting these values into the equation, we get:
25 = 0 + 7.3t
Simplifying the equation:
7.3t = 25
t = 25 / 7.3
Using a calculator, the value of t is about 3.42 seconds.
Therefore, it takes approximately 3.42 seconds for the motorcycle to reach the same speed as the car.
To find the distance between the motorcycle and the car when the motorcycle reaches this speed, we can use another kinematic equation:
s = ut + (1/2)at^2
where:
s = distance
u = initial velocity
t = time
a = acceleration
Since u = 0 m/s for the motorcycle and it starts at rest, the equation simplifies to:
s = (1/2)at^2
Substituting the values:
s = (1/2) * 7.3 * (3.42)^2
Using a calculator, the value of s is about 44.5 meters.
Therefore, the motorcycle is approximately 44.5 meters away from the car when it reaches the same speed.