Question:
The velocity of a particle is $v = v_0 + gt + ft^2$. If its position is $x = 0$ at $t = 0$, then its displacement after unit time $(t = 1)$ is
The velocity of a particle is $v = v_0 + gt + ft^2$. If its position is $x = 0$ at $t = 0$, then its displacement after unit time $(t = 1)$ is
Updated On: Jul 31, 2023
- $v_0 + 2g + 3f$
- $v_0 + g/2 + f/3$
- $v_0 + g + f$
- $v_0 + g/2 + f$
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The Correct Option is B
Solution and Explanation
$\int\limits^{x}_{{0}}dx=\int\limits^{1}_{{0}}(V_0+gt+ft^2)dt$
$x=v_{0}+g\left(\frac{1}{2}\right)+f \left(\frac{1}{3}\right)$
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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.