Question

An army vehicle of mass $1000kg$ is moving with a velocity of $10m/s$ and is acted upon by a forward force of $1000N$ due to the engine and a retarding force of $500N$ due to friction. What will be its velocity after $10s$

• A. $5m/s$
• B. $10m/s$
• C. $15m/s$
• D. $20m/s$

Answer 1

The correct option is C

$15m/s$

Step 1. Given data:

Mass of the army vehicle, $m=1000kg$

The initial velocity of the vehicle, $u=10m/s$

The forward force, $F=1000N$

The retarding force, $f=500N$

Time, $t=10s$

Step 2. Formula used:

The equation of motion, $v=u+at.......\left(1\right)$

where, $"v"$ is the final velocity in $m/s$

$"u"$ is initial velocity in $m/s$

$"a"$ is acceleration in $m/s^2$

$"t"$is time in $seconds$

Step 3. Finding the velocity of the army vehicle after $10s$

The acceleration of the vehicle in the forward direction is,

$a=\frac{F-f}{m}=\frac{1000-500}{1000}=0.5m/s^2$

Using equation $\left(1\right)$, we get

$$\begin{gathered} v=10+(0.5\times 10)m/s \\ v=(10+5)m/s \end{gathered}$$

$\therefore$ The final velocity after $10s$ will be $v=15m/s$

Hence, option C is correct.