To calculate the deceleration of the vehicle, we first need to determine the initial velocity of the vehicle before it started to decelerate. We can use the kinetic energy of the vehicle to find its initial velocity as follows:
Kinetic energy = (1/2) * mass * velocity^2
800000 J = (1/2) * 820 kg * velocity^2
velocity = sqrt((2 * 800000 J) / (820 kg)) = 34.93 m/s
So the initial velocity of the vehicle was 34.93 m/s.
Next, we can use the formula for acceleration to find the deceleration of the vehicle:
acceleration = (final velocity - initial velocity) / time
The final velocity of the vehicle is 20 m/s, the initial velocity is 34.93 m/s, and the time taken to decelerate is 8 seconds. Therefore:
acceleration = (20 m/s - 34.93 m/s) / 8 s = -1.86625 m/s^2
The negative sign indicates that the vehicle is decelerating, or slowing down.
Finally, we can calculate the resistance force using the resistance to motion and the mass of the vehicle:
resistance force = resistance to motion * mass = 0.262 N/kg * 820 kg = 214.04 N
We can use this resistance force to check our answer, by calculating the deceleration from the resistance force and the mass of the vehicle:
deceleration = resistance force / mass = 214.04 N / 820 kg = 0.2617 m/s^2
This value is very close to the value we calculated earlier, which confirms that our answer is correct.