Question

The position of an object moving along x-axis is given by x(t) = (4.2t
^2
+ 2.6)m, then find the
velocity of particle at t = 0 s and t = 3 s, then find the average velocity of particle at t = 0 s to
t = 3 s.​

Answer 1

Answer

Velocity at t = 0 s is 0 m/s

Velocity at t = s  is 25.2 m/s

Average velocity of particle at t = 0 s to t = 3 s is 8.4 m/s

Given

The position of an object moving along x-axis is given by x(t) = (4.2t ² +2.6) m

To Find

Velocity of particle at t=0 and t=3 s

Average velocity of particle at t=0 s to t=3 s

Solution

$\rm x=4.2t^2+2.6$

We know that , Instantaneous velocity is defined as distance travelled per particular instant of time .

$\to\ \rm v=\dfrac{dx}{dt}\\\\\to\ \rm v=\dfrac{d}{dt}(4.2t^2+2.6)\\\\\to\ \rm v=2(4.2)t+0\\\\\to\ \rm v=8.4t\\\\\to\ \rm v_{t=0}=8.4(0)\\\\\to\ \rm v_{t=0}=0\ m/s\ \; \bigstar\\\\\to\ \rm v_{t=3}=8.4(3)\\\\\to\ \rm v_{t=3}=25.2\ m/s\ \; \bigstar$

Now , we need to find average velocity of particle at t=0 s to t=3 s

$\to\ \rm A_{v}=\dfrac{v_{t=0}+v_{t=3}}{0+3}\\\\\to\ \rm A_{v}=\dfrac{0+25.2}{0+3}\\\\\to\ \rm A_{v}=\dfrac{25.2}{3}\\\\\to\ \rm A_{v}=8.4\ m/s\ \; \bigstar$