Question
A particle starts from rest and accelerates uniformly at 2 m/s² for 10 seconds. Calculate the distance covered and the final velocity attained.
A particle starts from rest and accelerates uniformly at 2 metres per second squared for a duration of 10 seconds. The problem requires us to calculate two things: the total distance covered during this time and the final velocity attained at the end of the motion. Since the particle starts from rest, its initial velocity is zero, and because the acceleration is uniform, we can apply the standard equations of motion without any modification.
This type of question is fundamental in kinematics because it combines two important concepts: acceleration and displacement. By solving it, we learn how to connect acceleration, time, velocity, and distance, which are the backbone of motion analysis. The scenario also reflects real-life physics — for example, a car accelerating from a stoplight or a ball rolling down an inclined plane under uniform acceleration.
Quick Answer
Final velocity = u + at = (0) + (2 × 10) = 20 m/s
Distance = ut + ½at² = (0 × 10) + ½(2)(10²) = 100 m
The particle attains a final velocity of 20 m/s and covers a distance of 100 metres.
Understanding the question with detailed explanations
The question clearly tells us the particle starts from rest. This means the initial velocity, u, is equal to zero. It then accelerates uniformly, meaning the rate of increase of velocity is constant throughout the 10 seconds. In physics, when we know acceleration, time, and initial velocity, we can calculate both the final velocity and the distance covered using the equations of motion.
The goal is not only to find the values but also to understand the process. Uniform acceleration makes the situation easier because we do not have to deal with varying rates of change or complicated calculus. All we need are the simple equations taught in the basics of kinematics. This makes the problem an excellent practice for beginners, while also providing a foundation for more complex motion problems in later studies.
A glimpse of the final answer
The calculation shows that after 10 seconds, the particle reaches a velocity of 20 metres per second. This means that at the end of the motion, the particle is moving quite quickly compared to when it started from rest. The distance covered in that same period is 100 metres, which is equivalent to the length of a standard running track straight section.
These numbers make sense when compared to real-world scenarios. For instance, if a small car were to accelerate steadily at 2 m/s² from rest, it could reach about 72 km/h (20 m/s × 3.6) in 10 seconds, which is realistic for many vehicles. Covering 100 metres in that time also aligns with what we might expect in sports or transport settings. This consistency reassures us that the answer is reasonable.
Data
From the problem:
• Initial velocity (u) = 0 m/s (since the particle starts from rest)
• Acceleration (a) = 2 m/s²
• Time (t) = 10 seconds
What we need:
• Final velocity (v) after 10 seconds
• Distance covered (s) during 10 seconds
Constants are not required here, since all quantities are already in SI units and no conversions are needed. The problem is fully defined by the given information.
Formula
The two relevant equations of motion are:
• Final velocity: v = u + at
• Distance covered: s = ut + ½at²
The first formula comes directly from the definition of acceleration as the rate of change of velocity. Since acceleration is uniform, the increase in velocity is linear with time. The second formula is derived from combining velocity and acceleration to find displacement under uniform acceleration.
Both formulas apply here because the motion starts from rest and is uniformly accelerated. No additional adjustments are needed, and we can substitute the given values directly.
Solution (solving the problem)
Step 1: Find the final velocity.
v = u + at
v = 0 + (2 × 10)
v = 20 m/s
Step 2: Find the distance covered.
s = ut + ½at²
s = (0 × 10) + ½(2)(10²)
s = 0 + 1 × 100
s = 100 m
Therefore, the final velocity attained is 20 m/s, and the distance covered is 100 m.
Final Answer
The particle attains a final velocity of 20 metres per second at the end of 10 seconds.
During this same time, the total distance covered by the particle is 100 metres. Both results are consistent with uniform acceleration and align perfectly with what the equations of motion predict.
Helpful Explanation
To visualise this, think of a car starting from rest at a traffic light. As it accelerates smoothly, it gets faster every second, and the distance it covers grows more and more each second. By the time 10 seconds have passed, the car is no longer creeping along — it is moving at a strong pace of 20 m/s. The total stretch it has travelled is 100 m, which is about the length of a standard football field.
A common mistake in such problems is forgetting to square the time in the displacement formula. Students sometimes write ½at instead of ½at², which gives the wrong result. Another error is to forget that u = 0 when the motion starts from rest. Always check the problem carefully for this condition. A good exam tip is to write down all known values first, then choose the equation that links them directly to the unknowns. This ensures you apply the right formula with fewer chances of error.