To find the average retarding force on the three-wheeler, we first need to determine the vehicle's initial speed in meters per second, calculate the deceleration, and then apply Newton's second law of motion. Let's break this down step by step.
Step 1: Convert Speed to Meters per Second
The initial speed of the three-wheeler is given as 36 km/h. To convert this to meters per second, we use the conversion factor where 1 km/h is equal to 1/3.6 m/s.
So, the calculation is:
- Initial speed (vi) = 36 km/h × (1/3.6) = 10 m/s
Step 2: Calculate Deceleration
The vehicle comes to rest in 4.0 seconds, which means the final speed (vf) is 0 m/s. We can find the deceleration (a) using the formula:
a = (vf - vi) / t
Substituting the values:
- a = (0 m/s - 10 m/s) / 4.0 s = -2.5 m/s²
The negative sign indicates that this is a deceleration, or retarding force.
Step 3: Calculate the Total Mass
The total mass (m) of the three-wheeler and the driver is the sum of their individual masses:
- Mass of the three-wheeler = 400 kg
- Mass of the driver = 65 kg
- Total mass (m) = 400 kg + 65 kg = 465 kg
Step 4: Apply Newton's Second Law
According to Newton's second law, the force (F) can be calculated using the formula:
F = m × a
Now, substituting the values we have:
- F = 465 kg × (-2.5 m/s²) = -1162.5 N
The negative sign indicates that the force is acting in the opposite direction of the motion, which is expected for a retarding force.
Final Result
The average retarding force on the vehicle is approximately 1162.5 N acting in the direction opposite to the motion. This force is crucial for stopping the vehicle in time to avoid an accident with the child.
