91Ó°ÊÓ

Acceleration is a measure of how quickly velocity changes. When acceleration is constant, it means that the rate at which velocity changes does not vary over time. This is a common scenario in kinematics, allowing us to apply straightforward mathematical equations to predict motion.

The constant acceleration in our problem is provided as 2.5 m/s². This means that every second, the motorcycle's speed increases by 2.5 meters per second in a straight line. When dealing with constant acceleration, we can use certain equations of motion to calculate other motion parameters such as velocity and time, as these relationships remain linear and predictable. Constant acceleration simplifies calculations as we don't have to account for any changes in acceleration over time.

Velocity refers to the speed of an object in a given direction. It is a vector quantity, meaning both magnitude and direction matter. In our scenario, velocity is adjusted, going from an initial value to a final value. The motorcycle, for instance, experiences velocity changes from 21 m/s to 31 m/s in part (a), and from 51 m/s to 61 m/s in part (b).

The change in velocity ( "Δv" ) is calculated by subtracting the initial velocity ( "u" ) from the final velocity ( "v" ). This change can then be utilized in conjunction with the known constant acceleration ( "a" ) to determine how long the change will take. These calculations help illustrate how quickly an object can respond to its acceleration, providing insight into its motion characteristics.

Calculating the time required for a velocity change under constant acceleration involves a straightforward manipulation of one of the primary kinematic equations. The appropriate equation is:\[ t = \frac{v - u}{a} \]where:

• "t" is the time,
• "v" is the final velocity,
• "u" is the initial velocity,
• "a" is the acceleration.

In our example, knowing the initial and final velocities along with the constant acceleration, helps plug in these values into the formula readily. For both parts (a) and (b), the change in velocity is 10 m/s, and dividing by the acceleration of 2.5 m/s² gives a time of 4 seconds. The calculation is direct because the values of velocity and acceleration are constant and uniform.

Equations of motion form the backbone of solving kinematics problems involving constant acceleration. The primary equations include:

• \( v = u + at \)
• \( s = ut + \frac{1}{2}at^2 \)
• \( v^2 = u^2 + 2as \)

In the context of our exercise, we focused on the first equation, which directly links the change in velocity to time and constant acceleration. Each equation serves a specific purpose depending on the known quantities and what needs to be calculated. While the second equation is used for calculating the displacement, and the third for velocities, acceleration, or displacement, here, we rearranged the first equation to isolate time, crucial for solving our specific problem.

By understanding the equations of motion, students can intuitively solve various kinematic scenarios, envisioning how different factors like time, velocity, and acceleration interrelate and affect an object's journey.