how large a fore (in newtons) is needed to accelerate a 5 metric-ton vehicle from rest to a speed of 10 km/hr in 4 s?
f=ma=m(vf-vi)/time
change vf to m/s
To calculate the force required to accelerate an object, we can use Newton's second law of motion, which states that the force (F) is equal to the mass (m) multiplied by the acceleration (a). In this case, we need to find the force required to accelerate the vehicle from rest to a speed of 10 km/hr in 4 seconds.
Step 1: Convert the mass to kilograms
The mass of the vehicle is given as 5 metric tons. Since 1 metric ton is equal to 1000 kilograms, we can convert this mass as follows:
Mass (m) = 5 metric tons × 1000 kg/metric ton = 5000 kg
Step 2: Convert the speed to meters per second
Given speed = 10 km/hr
To convert from kilometers per hour to meters per second, we need to multiply by a conversion factor.
Conversion factor: 1 km/hr = 1000 m / 3600 s
Speed in meters per second = 10 km/hr × (1000 m/3600 s) = 2.778 m/s (rounded to 3 decimal places)
Step 3: Calculate the acceleration
Acceleration (a) = Change in velocity / Time
Change in velocity = Final velocity - Initial velocity
Since the vehicle starts from rest, the initial velocity is 0 m/s.
Acceleration (a) = (2.778 m/s - 0 m/s) / 4 s = 0.6945 m/s^2 (rounded to 4 decimal places)
Step 4: Calculate the force
Force (F) = mass (m) × acceleration (a)
Force (F) = 5000 kg × 0.6945 m/s^2 = 3,472.5 N
Therefore, a force of approximately 3,472.5 Newtons (N) is needed to accelerate the 5 metric-ton vehicle from rest to a speed of 10 km/hr in 4 seconds.