To solve a numerical problem related to motion in one dimension, follow these steps:



Read the problem carefully and identify the given information and what needs to be calculated. Draw a diagram if necessary.



Identify the equations that can be used to solve the problem. The equations for motion in one dimension are:

- v = u + at
- s = ut + 0.5at^2
- v^2 = u^2 + 2as

where v is final velocity, u is initial velocity, a is acceleration, t is time, and s is displacement.



Substitute the given values into the relevant equation(s) and solve for the unknown(s). Make sure to use the correct units and round off the answer to the appropriate number of significant figures.



Check the answer to make sure it makes sense and is reasonable. If possible, check the answer using a different method or by estimating the answer.



A car accelerates from rest at a rate of 4 m/s^2 for 10 seconds. What is its final velocity and displacement?



Step 1: Understand the Problem

Given: u = 0 m/s, a = 4 m/s^2, t = 10 s

Unknown: v, s

Step 2: Determine the Relevant Equations

The relevant equations are:

- v = u + at
- s = ut + 0.5at^2

Step 3: Solve the Problem

Using the first equation:

v = u + at
v = 0 + 4(10)
v = 40 m/s

Using the second equation:

s = ut + 0.5at^2
s = 0(10) + 0.5(4)(10)^2
s = 200 m

Step 4: Check the Answer

The answer for the final velocity is 40 m/s, which is reasonable since the car has been accelerating for 10 seconds. The answer for the displacement is 200 m, which is also reasonable since the car has been accelerating for 10 seconds at a constant rate.