Question

A car moving along a straight line with an initial velocity of $25m{s}^{-1}$ north has a constant acceleration of $5m{s}^{-2}$ south. After $7s$ the velocity of the car will be _______________.

Answer 1

Acceleration:

• Acceleration can be defined as the rate of change of velocity with respect to time.
• It is a vector quantity.
• SI unit of acceleration is ms^-2

Step 1: Given data

Initial velocity, $u=25m{s}^{-1}$

Time, $t=7s$

Acceleration, $a=-5m{s}^{-2}$(due to negative direction)

(Note: The north direction is considered positive and the south direction negative.)

Step 2: Calculate the velocity of the car after $\mathbf{7}\mathbf{}\mathit{s}$

Let us assume the final velocity as $vm{s}^{-1}$. The first equation of motion is $\mathit{v}\mathbf{=}\mathit{u}\mathbf{+}\mathit{a}\mathit{t}$
Put the given values in the equation,

$$\begin{gathered} v=25+(-5)\times 7 \\ v=25-35 \\ v=-10m{s}^{-1} \end{gathered}$$
The negative sign represents that the final velocity is in the south direction.

Thus, after $7s$, the velocity of the car will be $\mathbf{10}\mathbf{}\mathit{m}{\mathit{s}}^{\mathbf{-}\mathbf{1}}$ south.