How much force is required to accelerate a 150 kg motorbike from 10 m/s to 20 m/s over a distance of 25 m? (assume no friction) the answer is 900 N Do not use kinematic equations
In accelerating from v=a to v=b, you have
b^2 - a^2 = 2as = 2a(F/m)s
Plug in your numbers
To determine the force required to accelerate the motorbike, we can use the concept of work and energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
In this case, the initial kinetic energy of the motorbike is given by the equation:
KE1 = (1/2) * mass * velocity1^2
where mass is the mass of the motorbike (150 kg) and velocity1 is the initial velocity (10 m/s).
The final kinetic energy of the motorbike is given by:
KE2 = (1/2) * mass * velocity2^2
where velocity2 is the final velocity (20 m/s).
The change in kinetic energy is then:
ΔKE = KE2 - KE1 = (1/2) * mass * velocity2^2 - (1/2) * mass * velocity1^2
ΔKE = (1/2) * mass * (velocity2^2 - velocity1^2)
Substituting the given values:
ΔKE = (1/2) * 150 kg * ((20 m/s)^2 - (10 m/s)^2)
Simplifying:
ΔKE = (1/2) * 150 kg * (400 m^2/s^2 - 100 m^2/s^2)
= (1/2) * 150 kg * 300 m^2/s^2
= 22,500 kg·m^2/s^2
The work done on the motorbike is equal to the change in kinetic energy, so:
Work = ΔKE = 22,500 kg·m^2/s^2
Since work is defined as force multiplied by distance, we have:
Work = force * distance
Rearranging the equation to solve for force:
force = Work / distance
Substituting the given distance of 25 m:
force = 22,500 kg·m^2/s^2 / 25 m
= 900 N
Therefore, the force required to accelerate the motorbike is 900 Newtons.
To calculate the force required to accelerate the motorbike, we need to use Newton's second law of motion, which is given by:
Force = mass x acceleration
Since the mass of the motorbike is 150 kg, and we need to find the force required to accelerate it from 10 m/s to 20 m/s over a distance of 25 m, we can determine the acceleration first.
The formula for acceleration can be derived from the following equation of motion:
v^2 = u^2 + 2as
where:
v = final velocity = 20 m/s
u = initial velocity = 10 m/s
s = distance = 25 m
Substituting the known values into the equation, we get:
(20 m/s)^2 = (10 m/s)^2 + 2a(25 m)
400 m^2/s^2 = 100 m^2/s^2 + 50a m
300 m^2/s^2 = 50a m
Dividing both sides by 50 m, we get:
6 m/s^2 = a
Now, we can substitute the mass (m = 150 kg) and acceleration (a = 6 m/s^2) into Newton's second law to find the force:
Force = mass x acceleration
Force = 150 kg x 6 m/s^2
Force = 900 N
Therefore, the force required to accelerate the motorbike is 900 N.