Question

A car travels in a straight line along a road. Its distance x from a stop sign is given as a function of time t by the equation 𝑥 = 2.0𝑡² − 0.50𝑡³. Calculate the distance of the car when it achieves its maximum speed in the positive x direction. 

Answer 1

To be asked in question

Maximum speed achieve ix +ive x direction =?

$x=2.0t^2-0.50t^3\rightarrow(1)$

Eqution (1) differenciate with respect to time

$v=\frac{dx}{dt}=4t-1.50t^2\rightarrow(2)$

Eqution (2) differenciate with respect to time

$a=\frac{dv}{dt}=4-3t\rightarrow(3)$

Maximum speed

a=0

$t=\frac{4}{3}$

At $t=\frac{4}{3}$ Velocity is maximum then

Displacement

Eqution (1)put values

$x=2\times(\frac{4}{3})^2-0.50\times(\frac{4}{3})^3$

$x=\frac{63}{27}=2.3703meter$