Position of a particle moving along x-axis is given by x=3 t-4 t2+t3, where x is in metre and t in seconds. Find the average velocity of the particle in the time interval from t =2 s to 4 s.

Question

Position of a particle moving along x-axis is given by x=3 t-4 t2+t3, where x is in metre and t in seconds. Find the average velocity of the particle in the time interval from t =2 s to 4 s. (A) 7 m/s (B) 9 m/s (C) 13 m/s (D) none of these

Tardigrade Admin · Accepted Answer

Rate of change of displacement is velocity,
i.e.,

v = \frac{d x}{d t} v = \frac{d x}{d t} = 3 - 8 t + 3 t^{2}

Given,

x = 3 t - 4 t^{2} + t^{3}

v = \frac{d x}{d t} = 3 - 8 t + 3 t^{2}

At

t = 2, v_{1} = 3 - 16 + 12 = - 1

At

t = 4, v_{2} = 3 - 32 + 48 = 19

Average velocity

= \frac{v _{1} + v _{2}}{2} = \frac{- 1 + 19}{2}

= 9 m / s

Q. Position of a particle moving along x-axis is given by x=3t−4t2+t3, where x is in metre and t in seconds. Find the average velocity of the particle in the time interval from t=2s to 4s.

7 m/s

9 m/s

13 m/s

none of these

Rate of change of displacement is velocity, i.e., v=dtdx​v=dtdx​=3−8t+3t2 Given, x=3t−4t2+t3 v=dtdx​=3−8t+3t2 At t=2,v1​=3−16+12=−1 At t=4,v2​=3−32+48=19 Average velocity =2v1​+v2​​=2−1+19​ =9m/s

Q. Position of a particle moving along $x$ -axis is given by $x = 3 t - 4 t^{2} + t^{3}$ , where $x$ is in metre and $t$ in seconds. Find the average velocity of the particle in the time interval from $t = 2 s$ to $4 s$ .