Q16CQ - College Physics (Urone)

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?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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.