A 275 kg motor cycle and rider accelerate from restand reach a velocity of 20m.s-1 West.the motor cycle wheels exert an average force of 710N East on the road. Calculate the minimum time taken to reach a velocity of 20m.s-1
To calculate the minimum time taken to reach a velocity of 20 m/s, we can use the equation:
Force = mass × acceleration
In this case, the force applied is 710 N, and the mass is the combined mass of the motorcycle and rider, which is 275 kg.
The acceleration can be calculated using Newton's second law of motion:
acceleration = Force / mass
Substituting the given values, we get:
acceleration = 710 N / 275 kg
Now, to find the time taken to reach the desired velocity, we can use the equation:
velocity = initial velocity + (acceleration × time)
In this case, the initial velocity is 0 m/s, the final velocity is 20 m/s, and we need to find the time.
Substituting the values into the equation, we have:
20 m/s = 0 m/s + (acceleration × time)
We can rearrange the equation to isolate time:
time = (20 m/s - 0 m/s) / acceleration
Now, we will substitute the value of acceleration calculated earlier:
time = (20 m/s - 0 m/s) / (710 N / 275 kg)
By simplifying the equation, we get:
time = (20 m/s) × (275 kg / 710 N)
Now we can calculate the minimum time taken to reach a velocity of 20 m/s:
time = (20 × 275) / 710
time ≈ 7.76 seconds
Therefore, the minimum time taken to reach a velocity of 20 m/s is approximately 7.76 seconds.
To calculate the minimum time taken to reach a velocity of 20 m/s, we can use Newton's second law of motion, which states that the force applied (F) is equal to the mass (m) multiplied by the acceleration (a).
In this case, the force exerted by the motorcycle wheels (710 N) is acting in the opposite direction to the desired velocity (East), so the force should be negative (-710 N).
We can rearrange the formula to solve for acceleration (a):
F = m * a
a = F / m
Now we can calculate the acceleration:
a = (-710 N) / (275 kg + rider)
The mass of the motorcycle is given as 275 kg, but the mass of the rider is not specified in the question. Therefore, we need to know the mass of the rider to obtain an accurate answer.
a = 710/275
v = a t
t = 20 * 275 / 710 seconds