Question

The velocity of a body at any instant is $10\;ms^{-1}$. After 5sec, velocity of the particle is $20\;ms^{-1}$. The velocity at 3sec before is (assume uniform acceleration):
$8\;ms^{-1}$
$4\;ms^{-1}$
$6\;ms^{-1}$
$7\;ms^{-1}$

Answer 1

Recall a kinematic equation of motion that relates velocity, time and uniform acceleration. Use this relation to first determine the acceleration with which the body executes its motion. Then, given that the body accelerates uniformly, use the same equation of motion using the instantaneous velocity of the body to determine the velocity at the given time.
Formula Used: Kinematic equation of motion $v=u+at$

Complete step-by-step solution:
Let us write down the given information,
$u=10m{{s}^{-1}},t=5s,v=20m{{s}^{-1}}$
Applying the newton's equation of motion, we get,
$\begin{aligned} & v=u+at \\\ & \Rightarrow 20=10+a(5) \\\ & \Rightarrow a=\dfrac{20-10}{5}m{{s}^{-2}} \\\ & \therefore a=2m{{s}^{-2}} \\\ \end{aligned}$
Now, the question is given that the acceleration throughout the motion is uniform, meaning the acceleration does change at all. So, we can use the acceleration obtained in the calculation of the second case.
In the second case,
$\begin{aligned} & v=10m{{s}^{-1}},t=3s,a=2m{{s}^{-2}} \\\ & v=u+at \\\ & \Rightarrow 10=u+(2\times 3) \\\ & \therefore u=4m{{s}^{-1}} \\\ \end{aligned}$
Hence, in this way, we can find the unknown velocity of a body when all other required terms are given using the newton's equation of motion.
Additional information:
Equations of motion of kinematics describe the basic concept of the motion of an object such as the position, velocity, or acceleration of an object at various times. These three equations of motion govern the motion of an object in 1D, 2D, and 3D. The derivation of the equations of motion is one of the most important topics in Physics. There are three equations of motion that can be used to derive components such as displacement(s), velocity (initial and final), time(t), and acceleration(a).

Note: In the above question, it is given that the acceleration of the body throughout the motion is uniform, which means acceleration is constant and will not change. If it wasn’t given, the acceleration for the second case will be different from that of the first one.