A car traveling at 35 m/s suddenly accelerates to a new speed of 56.5 m/s in a time of 5.0 seconds. A) What is its acceleration? B) If the car had a mass of 2200 kg, what was the applied traction force necessary for it to accelerate? Assume NO resistance!
A. V = Vo + a*t.
56.5 = 35 + a*5,
a = ?
B. F = M*a.
To solve this problem, we'll use the formula for acceleration:
Acceleration (a) = (Change in velocity) / (Time taken)
A) To find the acceleration of the car, we need to calculate the change in velocity and divide it by the time taken.
Change in velocity = Final velocity - Initial velocity
Change in velocity = 56.5 m/s - 35 m/s
Change in velocity = 21.5 m/s
Time taken = 5.0 seconds
Now, we can calculate the acceleration:
Acceleration = 21.5 m/s / 5.0 seconds
Acceleration = 4.3 m/s²
Therefore, the acceleration of the car is 4.3 m/s².
B) To find the applied traction force necessary for the car to accelerate, we'll use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration:
Force = Mass * Acceleration
Mass = 2200 kg
Acceleration = 4.3 m/s² (from part A)
Now, we can calculate the force:
Force = 2200 kg * 4.3 m/s²
Force = 9460 N
Therefore, the applied traction force necessary for the car to accelerate is 9460 N.