A motorcycle traveling 92.0 km/hr approaches a car traveling in the same direction at 82.0 km/hr. When the motorcycle is 51.0 m behind the car, the rider accelerates and passes the car 15.0 s later. What is the acceleration of the motorcycle (in meters/second^2)?
(v * t) + (1/2 * a * t^2) = V * t
convert the motorcycle (v) and car (V) velocities to m/s
To find the acceleration of the motorcycle, we need to determine its initial velocity, final velocity, and the time taken to accelerate.
First, let's convert the velocities to meters per second (m/s):
- The motorcycle's initial velocity is 92.0 km/hr, which is equivalent to (92.0 * 1000) / 3600 m/s = 25.56 m/s.
- The car's velocity is 82.0 km/hr, which is equivalent to (82.0 * 1000) / 3600 m/s = 22.78 m/s.
Next, we can determine the time taken to accelerate by subtracting the time it took for the motorcycle to overtake the car (15.0 s) from the time it took for the motorcycles to close the initial gap between the car and itself.
To close the initial distance gap of 51.0 m, the motorcycle needs to cover this distance at the relative speed between the motorcycle and the car:
Relative speed = motorcycle's initial velocity - car's velocity
Relative speed = 25.56 m/s - 22.78 m/s = 2.78 m/s
Now, we can calculate the time taken to close this gap:
Time = Distance / Relative speed
Time = 51.0 m / 2.78 m/s ≈ 18.35 s
Since the total time taken is the time to close the gap plus the additional 15.0 s, the elapsed time is:
Total time taken = Time to close the gap + Additional time
Total time taken = 18.35 s + 15.0 s = 33.35 s
Finally, we can calculate the acceleration using the equation:
Acceleration = (Final velocity - Initial velocity) / Time
Acceleration = (0 m/s - 25.56 m/s) / 33.35 s ≈ -0.77 m/s^2
Therefore, the acceleration of the motorcycle is approximately -0.77 m/s^2. The negative sign indicates that the motorcycle is decelerating.