How large a force (in newtons) is needed to accelerate a 3 metric-ton vehicle from rest to a speed of 50 km/hr in 4 s?
M = 3 metric tons = 3000 kg
top speed = 50 km/h = 13.89 m/s
acceleration = a = 13.89/4.0
= 3.47 m/s^2
Now use F = M a for the force in newtons
3000 kg x 3.47 m/s^2 but the answer is wrong.
To determine the force required to accelerate a vehicle, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
Force = mass * acceleration
First, we need to convert the mass of the vehicle from metric tons to kilograms since the SI unit of mass is kilograms.
1 metric ton = 1000 kilograms
So, the mass of the vehicle is:
Mass = 3 metric tons * 1000 kg/metric ton = 3000 kg
Next, we need to calculate the acceleration. We can use the kinematic equation that relates acceleration, final velocity, initial velocity, and time:
final velocity = initial velocity + (acceleration * time)
We are given the initial velocity (rest) as 0 km/hr, the final velocity as 50 km/hr, and the time as 4 seconds.
Let's convert the velocities to m/s to match the SI unit:
0 km/hr = 0 m/s
50 km/hr = 50 * (1000 m/3600 s) = 13.89 m/s
Now we can rearrange the equation to solve for acceleration:
acceleration = (final velocity - initial velocity) / time
acceleration = (13.89 m/s - 0 m/s) / 4 s = 3.4725 m/s^2
Now, we can substitute the values of mass and acceleration into Newton's second law to find the force:
Force = 3000 kg * 3.4725 m/s^2 = 10,417.5 N
Therefore, a force of 10,417.5 Newtons is needed to accelerate the 3 metric-ton vehicle from rest to a speed of 50 km/hr in 4 seconds.