Question

A car of mass 1000 kg is moving with velocity of \[10m{{s}^{-1}}\] and is acted upon by a forward force of 1000 N due to the engine and retarding force of 500 N. The velocity after 10 seconds will be:
A. \[10m{{s}^{-1}}\]
B. \[15m{{s}^{-1}}\]
C. \[20m{{s}^{-1}}\]
D. Zero

Answer 1

Hint: Kinematic equations can be used to find the final velocity of the car. Here the retarding force is considered as the frictional force. To solve the given problem.
Formula used: Force on the car, \[{{F}_{C}}=ma\], where m is the mass of the car and a is the acceleration.
\[V=u+at\], where V is the final velocity, u is the initial velocity, a is the acceleration and t is the time for the travel.

Complete step by step answer:
First, we can write the given information from the question.
Mass of the car, \[m=1000kg\]
The velocity of the car, \[u=10m{{s}^{-1}}\]
Forward force on the car due to engine, \[F=1000N\]
Here, we can call the retarding force as the frictional force, \[f=500N\]
Time is taken for the travel, \[t=10s\]
So the net force \[({{F}_{C}})\] on the car will be,
\[{{F}_{C}}=1000N-500N\]
\[{{F}_{C}}=500N\]
From this force, we can find out the acceleration of the car.
\[{{F}_{C}}=ma\], where m is the mass of the car and a is the acceleration.
\[a=\dfrac{{{F}_{C}}}{m}\]
\[a=\dfrac{500}{1000}\]
\[a=0.5m{{s}^{-2}}\]
We can use the kinematic equation, to find the final velocity of the car.
\[V=u+at\], where V is the final velocity, u is the initial velocity, a is the acceleration and t is the time for the travel.
\[V=10+0.5\times 10\]
\[V=15m{{s}^{-1}}\]
Hence the correct option is B.
Additional information: With these following kinematic equations, you can solve all most of the problems related to motion.
\[{{v}^{2}}-{{u}^{2}}=2aS\]
\[\begin{align}
  & v=u+at \\
 & S=ut+\dfrac{1}{2}a{{t}^{2}} \\
 & S=\left[ \dfrac{u+v}{2} \right]t \\
\end{align}\]
where v is the final velocity, u is the initial velocity, t is the time, S is the displacement and a is the acceleration.
Note: In the question, two forces are acting on the car. So we have to find the net force. If it is acting in the same direction it has to be added. Otherwise, find the difference between them. From the question itself, you can see the forwarding force is more than that of the retarding force. So the final velocity will be more than that of the initial velocity.