Question

If a body is moving under non-uniform acceleration of a=bt,give the equation for the final velocity ‘u’,time ‘t’ and acceleration.

Answer 1

Answer : Final velocity, $v=\dfrac{bt^2}{2}+u$

Explanation :

It is given that the body is moving under non uniform acceleration, a = bt

We know that the acceleration of an object is defined as the rate of change of velocity.

$a=\dfrac{v-u}{t}$

where

u is the initial velocity.

v is the final velocity

t is the time taken.

$a=\dfrac{dv}{dt}$

$bt=\dfrac{dv}{dt}$

$\int\limits^t_0 {bt\ dt} =\int\limits^v_u {dv}$

$\dfrac{bt^2}{2}=v-u$

$v=\dfrac{bt^2}{2}+u$

This is the expression of final velocity.

Hence, this is the required solution.

Answer 2

answer : $\boxed{u+\frac{bt^2}{2}}$

given, a = bt

here it is given that, acceleration is variable function. so, finding velocity we have to use integration method.

we know, acceleration is the rate of change of velocity per unit time.

e.g., a = dv/dt

so, dv/dt = a = bt

$\int{dv}=\int{bt}\,dt\\\\\int\limits^v_u=\int\limits^t_0{bt}\,dt\\\\v-u=\frac{bt^2}{2}\\\\v=u+\frac{bt^2}{2}$

hence, final velocity of the body is v = u + bt²/2