Question:

An auto travelling along a straight road increases its speed from $30.0\, m \,s^{-1}$ to $50.0 \,m \,s^{-1}$ in a distance of $180 \,m$. If the acceleration is constant, how much time elapses while the auto moves this distance ?

Updated On: Jul 6, 2022
  • $6.0\,s$
  • $4.5\,s$
  • $3.6\,s$
  • $7.0\,s$
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The Correct Option is B

Solution and Explanation

Let a be constant acceleration of auto. Here, $u = 30 \,m\, s^{-1}$, $v = 50 \,m \,s^{-1}$, $S = 180 \,m$ As $v^2-u^2=2aS$ $\left(50\right)^{2}-\left(30\right)^{2}=2\times a\times 180$ $\therefore a=\frac{1600}{2\times180}=\frac{40}{9} m\,s^{-2}$ As $S=ut+\frac{1}{2} at^{2}$ $\Rightarrow 180=30\times t+\frac{1}{2}\times\frac{40}{9}\times t^{2}$ $\Rightarrow 2t^{2}+27t-162=0$ Solving this quadratic equation by quadratic formula, we get $= 4.5\ s$, $- 18 \,s$, ($t$ can?? be negative) $\therefore. t = 4.5 \,s$
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Notes on Motion in a straight line

Concepts Used:

Motion in a straight line

The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion. 

Types of Linear Motion:

Linear motion is also known as the Rectilinear Motion which are of two types:

  1. Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
  2. Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.