If there is a constant towing force of 1.5 kN, how long would it take a tow truck to tow a 1400 kg car from rest to 52 km/h?
(Assume a rolling resistance of 215 N).
net force=mass*acceleration
1500-215= 1400(acceleration)
then, vfinal=a *time
change 52km/hr to m/s before you start.
To find the time it takes for the tow truck to tow the car from rest to a certain speed, we can use the principle of Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
First, we need to determine the net force acting on the car. The net force is the sum of the towing force and the rolling resistance force.
1. The towing force is given as 1.5 kN, which is equal to 1500 N.
2. The rolling resistance force is given as 215 N.
Therefore, the net force is:
Net force = Towing force - Rolling resistance force = 1500 N - 215 N = 1285 N.
Next, we can calculate the acceleration of the car using Newton's second law:
Net force = mass * acceleration.
Rearranging the equation, we have:
Acceleration = Net force / mass = 1285 N / 1400 kg = 0.918 m/s^2.
Now, we can find the time it takes for the car to reach a speed of 52 km/h. First, we need to convert the speed from km/h to m/s:
52 km/h * (1000 m/1 km) * (1 h / 3600 s) = 14.4 m/s.
Using the equation for constant acceleration, where final velocity (v) is equal to initial velocity (u) plus acceleration (a) multiplied by time (t):
v = u + at.
Since the car starts from rest (u = 0), the equation simplifies to:
v = at.
Rearranging the equation to solve for time, we have:
t = v / a = 14.4 m/s / 0.918 m/s^2 ≈ 15.71 seconds.
Therefore, it would take approximately 15.71 seconds for the tow truck to tow the 1400 kg car from rest to a speed of 52 km/h.