A body moving in a straight line speeds up from an initial velocity of 25 m/s to a final velocity of 30 m/s in 10 seconds. What is the magnitude of its acceleration in m/s^2?

Introduction / Context:
Acceleration is the rate of change of velocity with respect to time. It is a core concept in kinematics and dynamics. This question provides initial and final velocities and the time taken for the change, then asks you to calculate the acceleration. Such straightforward problems reinforce how to use the basic definition of acceleration in numerical form.

Given Data / Assumptions:

• Initial velocity u = 25 m/s.
• Final velocity v = 30 m/s.
• Time interval t = 10 seconds.
• Motion is along a straight line and acceleration is assumed constant during this interval.

Concept / Approach:
For motion with constant acceleration, the acceleration a is defined as the change in velocity divided by the time taken: a = (v - u) / t Here, v is the final velocity, u is the initial velocity, and t is the time interval. Positive values of a indicate speeding up in the direction of motion, while negative values indicate slowing down.

Step-by-Step Solution:
Step 1: Write the formula for acceleration: a = (v - u) / t. Step 2: Substitute the given values: u = 25 m/s, v = 30 m/s, and t = 10 s. Step 3: Compute the change in velocity: v - u = 30 - 25 = 5 m/s. Step 4: Divide by the time: a = 5 / 10 = 0.5 m/s^2. Step 5: Therefore, the acceleration magnitude is 0.5 m/s^2.

Verification / Alternative check:
If the body increases its speed by 5 m/s over 10 seconds, then each second the speed increases by 0.5 m/s on average. This intuitive interpretation matches the calculated acceleration of 0.5 m/s^2. The units also work out correctly: (m/s) divided by s gives m/s^2, which is the correct unit for acceleration.

Why Other Options Are Wrong:

• 5.5 m/s^2: This is much larger than the correct value and cannot be obtained by correctly applying the formula.
• 1 m/s^2: This would correspond to a 10 m/s increase in velocity over 10 seconds, which does not match the given data.
• 11 m/s^2: This would require a very large change in velocity over a short time and is incompatible with the numbers given in the question.

Common Pitfalls:
Errors often arise from reversing u and v, leading to incorrect signs, or from dividing the wrong way round, such as t / (v - u). Some students also forget to include the correct units in the final answer. Always remember that acceleration is change in velocity per unit time and that the direction and sign can be important in more complex problems.

Final Answer:
The acceleration of the body is 0.5 m/s^2.