Question:
A car starts from rest and travels with uniform acceleration $\alpha$ for some time and then With uniform retardation $\beta$ and comes to rest If the total time of travel of the car is 't' the maximum velocity attained by it is given by
A car starts from rest and travels with uniform acceleration $\alpha$ for some time and then With uniform retardation $\beta$ and comes to rest If the total time of travel of the car is 't' the maximum velocity attained by it is given by
Updated On: Jul 5, 2022
- $\frac{\alpha \beta}{(\alpha+\beta)} t$
- $\frac{1}{2}\frac{\alpha \beta}{(\alpha+\beta)} t^2$
- $\frac{\alpha \beta}{(\alpha-\beta)} t$
- $\frac{1}{2}\frac{\alpha \beta}{(\alpha-\beta)} t^2$
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The Correct Option is A
Solution and Explanation
maximum velocity $\nu = \alpha t_1 = \beta t_2$ and $t = t_1 + t_2$
$\Rightarrow \, \frac{\nu}{\alpha} + \frac{\nu}{\beta} = t = \Rightarrow \nu = \frac{(\alpha \beta)t}{(\alpha + \beta)}$
S = $ut + \frac{1}{2} at^2$
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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:
- 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.
- 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.