If a car starts from rest and its velocity becomes 30 m/s in 12 seconds, then find the acceleration.
Answer (1)
Identify the initial velocity ( v 0 = 0 m/s), final velocity ( v f = 30 m/s), and time ( t = 12 s).
Apply the formula for acceleration: a = t v f − v 0 .
Substitute the given values into the formula: a = 12 30 − 0 .
Calculate the acceleration: a = 2.5 m/s 2 . The acceleration of the car is 2.5 m/s 2 .
Explanation
Problem Analysis The problem states that a car starts from rest and reaches a velocity of 30 m/s in 12 seconds. We need to find the acceleration of the car.
Formula and Given Values We are given:
Initial velocity, v 0 = 0 m/s
Final velocity, v f = 30 m/s
Time taken, t = 12 s
The formula for acceleration is: a = t v f − v 0
Calculation Substitute the given values into the formula: a = 12 s 30 m/s − 0 m/s a = 12 30 m/s 2 a = 2.5 m/s 2
Final Answer The acceleration of the car is 2.5 m/s 2 .
Examples
Understanding acceleration is crucial in many real-world scenarios. For instance, when designing a car, engineers need to calculate the acceleration to ensure it meets performance standards and safety requirements. Knowing the acceleration helps determine how quickly a car can reach a certain speed, which is important for merging onto highways or avoiding collisions. Similarly, in sports, understanding acceleration helps athletes optimize their performance, whether it's a sprinter improving their start or a baseball player increasing their bat speed.
