Calculating Acceleration and Force of a Toyoda Car

Consider a new automobile by the Toyoda Corporation (Toyota) that has a mass of 2000 kg and starts from rest. The car reaches a speed of 160 meters per second in 30 seconds. This article explains how to calculate the car's acceleration and the force required to achieve this acceleration, using Newton's second law of motion.

Calculation of Acceleration

Acceleration can be calculated using the formula:

a  frac{Delta v}{Delta t}

Where:

a is the acceleration Delta v is the change in velocity Delta t is the change in time

Given:

Initial velocity v_i 0 m/s (since it starts from rest) Final velocity v_f 160 m/s Time interval Delta t 30 seconds

Change in Velocity Calculation

The change in velocity is calculated as:

Delta v  v_f - v_i  160 m/s - 0 m/s  160 m/s

Substituting Values into the Acceleration Formula

Substituting the values into the acceleration formula, we get:

a  frac{160 m/s}{30 s} approx 5.33 m/s^2

Therefore, the acceleration of the car is approximately 5.33 m/s^2.

Calculation of Force

According to Newton's second law of motion (F ma), the force can be calculated using the formula:

F  ma

Where:

F is the force m is the mass a is the acceleration

Given:

Mass m 2000 kg Acceleration a 5.333 m/s^2

Force Calculation

The force required to achieve this acceleration is calculated as:

F  2000 kg * 5.333 m/s^2  10666 N

Therefore, the force required to accelerate the car is approximately 10666 N.

Conclusion

In this article, we have calculated the acceleration and force of a Toyoda car that reaches a speed of 160 meters per second in 30 seconds. The acceleration is approximately 5.33 m/s^2, and the force required to achieve this acceleration is approximately 10666 N. These calculations are crucial for engineers and automotive enthusiasts to understand the performance specifications of cars.