If the velocity of an object changes from 65 m/s to 98 m/s during a time interval of 12 s, what's the acceleration of the object?
A. 13.58 m/s
B. 33 m/s
C. 2.75 m/s
D. 5.42 m/s
Answer (2)
Define acceleration as the rate of change of velocity with respect to time: a = Δ t Δ v .
Substitute the given values: v i = 65 m/s, v f = 98 m/s, and Δ t = 12 s into the formula.
Calculate the acceleration: a = 12 98 − 65 = 12 33 = 2.75 m/s².
The acceleration of the object is 2.75 m/s 2 .
Explanation
Understanding the Problem We are given the initial velocity, final velocity, and the time interval over which the velocity changes. We need to find the acceleration of the object.
Stating the Formula Acceleration is defined as the rate of change of velocity with respect to time. The formula for acceleration is: a = Δ t Δ v = Δ t v f − v i where:
a is the acceleration,
Δ v is the change in velocity,
Δ t is the time interval,
v f is the final velocity, and
v i is the initial velocity.
Calculations We are given:
Initial velocity, v i = 65 m/s
Final velocity, v f = 98 m/s
Time interval, Δ t = 12 s Substitute these values into the formula: a = 12 98 − 65 a = 12 33 a = 2.75 m/s 2
Final Answer The acceleration of the object is 2.75 m/s². Therefore, the correct answer is OC.
Examples
Understanding acceleration is crucial in many real-world scenarios, such as designing vehicles or analyzing the motion of objects. For example, when designing a car, engineers need to calculate the acceleration required to reach a certain speed within a specific time frame. Similarly, understanding acceleration helps in analyzing the motion of projectiles, like a ball thrown in the air, where acceleration due to gravity plays a significant role. This concept is also fundamental in understanding Newton's laws of motion, which govern the movement of objects around us.
The acceleration of the object is calculated to be 2.75 m/s² using the formula for acceleration. This is determined by finding the change in velocity over the time interval. Therefore, the answer is option C.
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