Question

An object moves along x-axis such that its position varying with time t is given as x = 4t - t^2 (x is in metre and time t in second). the distance travelled by the object from t = 0 to t = 3 s is

Answer 1

Simply put the value of t and then subtract:-

$x_{0}= 4t-t^2\\x= 4*0 - 3^2 => 0$

Similarly,

Put $x=3$

$x_{3} = 4*3 - 3^2  => 3$

$x_{3} - x_{0}  = 3 meters$

Answer 2

Answer:

5m

Explanation:

x=4t-t²

dx/dt = 4-2t

4-2t=0

4=2t

t=2 sec.

At t=0 , x=0

At t=2 , x=(4*2)-(2)²

x=8-4=4m

At t=3 , x=(4*3)-(3)²

x=12-9=3m

So 0to4 Then 4to3

4+1=5m