Question

If a subway train is moving to the left (has a negative velocity) and then comes to a stop, what is the direction of its acceleration? Is the acceleration positive or negative?

Short answer

The acceleration will be in the right direction. The acceleration will be shown as positive.

Step-by-step solution

Acceleration and its direction

In terms of both speed and direction, acceleration is the rate at which velocity varies with time. Acceleration is a vector quantity since it has both a magnitude and a direction.

Acceleration of train

Here we have to consider the velocity of the train initially, which is moving in the left direction has magnitude V m/s and the direction can be negative sign ass mentioned in the question.

• The initial velocity of the train = $-V\text{\hspace{0.17em}m/s}$.
• The train is stopped after some time T.
• The final velocity of the train will be = $\text{0\hspace{0.17em}m/s}$.

Applying the formula of acceleration as:

$\begin{array}{l}\mathrm{a}=\frac{\mathrm{\Delta V}}{\mathrm{T}}\\ \mathrm{a}=\frac{\text{Final\hspace{0.17em}velocity\hspace{0.17em}}-\text{\hspace{0.17em}Intial\hspace{0.17em}velocity}}{\text{Time}}\\ \mathrm{a}=\frac{0-(-\mathrm{V})}{\mathrm{T}}\\ \mathrm{a}=\frac{\mathrm{V}}{\mathrm{T}}{\text{\hspace{0.17em}m/s}}^2\end{array}$

Hence it can be said that the train had a positive acceleration, which is opposite to that of the velocity of the train.