Question

A truck of mass 2800kg is moving with a speed of $15m{{s}^{-1}}$ . A frictional retarding force of 500N and forward force 1200N are acting on it, then in 10s it shall travel a distance of:

Answer 1

The distance travelled by the car after time ten seconds can be found using one of the newton's formulae of motion. We need to find the acceleration as the velocity, time is given in the question. The acceleration can be found by dividing the force with the mass of the object.
Formulas used:
$S=ut+\dfrac{1}{2}a{{t}^{2}}$

Complete answer:
As the mass of the truck is given, we can find the acceleration of the block by finding the net force acting on it and dividing the net force with the mass of the block.
So, the acceleration will be equal to,
$\begin{aligned} & a=\dfrac{F}{m} \\\ & \Rightarrow a=\dfrac{1200-500}{2800} \\\ & \Rightarrow a=\dfrac{1}{4}m{{s}^{-2}} \\\ \end{aligned}$
Now, the distance travel by the block in tens seconds can be calculated as,
$\begin{aligned} & S=ut+\dfrac{1}{2}a{{t}^{2}} \\\ & \Rightarrow S=150+\dfrac{1}{2}\times \dfrac{1}{4}\times 100 \\\ & \Rightarrow S=162.5m \\\ \end{aligned}$
Therefore, we can find the distance travelled in a given time in this way.

Additional information:
The relation between velocity and time is a simple one during uniformly accelerated, straight-line motion. The longer the acceleration, the greater the change in velocity. Change in velocity is directly proportional to time when acceleration is constant. If velocity increases by a certain amount in a certain time, it should increase by twice that amount in twice the time. If an object already started with a certain velocity, then its new velocity would be the old velocity plus this change. The displacement of a moving object is directly proportional to both velocity and time. Move faster. Go farther. Move longer (as in longer time). Go farther. Acceleration compounds this simple situation since velocity is now also directly proportional to time. Try saying this in words and it sounds ridiculous. "Displacement is directly proportional to time and directly proportional to velocity, which is directly proportional to time." Time is a factor twice, making displacement proportional to the square of time.

Note:
In the above equation, the net force is taken as the difference between the two forces because the frictional force always acts in the direction opposite to the forward force acting on the object. Also, Newton's equation of motion is only applicable if the frame of reference is constant.