Question

The position of a particle moving along x axis is given by x=10t—2t^2. Then the time at which it will momently come to rest is

Answer 1

When a particle comes to rest its velocity will be equal to 0. Therefore the derivative of the function should be equal to zero

$x = 10t - t^{2}$
$\frac{dx}{dt}=0$
[tex] \frac{dx}{dt}(10t - t^{2})=10-4t [/tex]
$10-4t=0 \\ 10=4t \\ t= \frac{10}{4}=2.5s$

Answer 2

When a particle comes to rest its velocity will be equal to 0. Therefore the derivative of the function should be equal to zero

x = 10t - t^{2}  

\frac{dx}{dt}=0  

\frac{dx}{dt}(10t - t^{2})=10-4t 


10-4t=0 \\ 10=4t \\ t= \frac{10}{4}=2.5s