A car accelerates uniformly from rest at 3$ms^{-2}$. its velocity after traveling a distance of 24m is

Analysis

To solve this problem, we need to identify the given parameters and select the appropriate kinematic equation that relates velocity, acceleration, and distance.

Given parameters:

• Initial velocity ($u$) = $0 \, ms^{-1}$ (since the car starts from rest)
• Acceleration ($a$) = $3 \, ms^{-2}$
• Distance ($s$) = $24 \, m$
• Final velocity ($v$) = ?

Concept

Since we are dealing with uniform acceleration and we have distance, initial velocity, and acceleration, we use the third equation of motion:

Solution

1. Substitute the known values into the formula: $$v^2 = (0)^2 + 2 \times 3 \times 24$$

2. Perform the multiplication: $$v^2 = 0 + 6 \times 24$$ $$v^2 = 144$$

3. Solve for $v$ by taking the square root of both sides: $$v = \sqrt{144}$$ $$v = 12 \, ms^{-1}$$

Conclusion

Comparing our result with the provided options, the correct velocity is $12 \, ms^{-1}$.

Exam Tip

Always check your units before starting. If the acceleration were in $km/h^2$ and distance in $km$, you would need to convert them to SI units ($m/s^2$ and $m$) before using the equations of motion. Also, remember that "from rest" always means $u = 0$, which simplifies your calculation significantly!