A particle moves in a straight line, its position (in m) as function of time is given by x = (at2 + b). What is average velocity in time interval t = 3 s to t = 5 sec? (Where a and b are constants and a = 1 m/s2, b = 1 m.)

Question

A particle moves in a straight line, its position (in m) as function of time is given by x = (at2 + b). What is average velocity in time interval t = 3 s to t = 5 sec? (Where a and b are constants and a = 1 m/s2, b = 1 m.) (A) 8 ,m/s (B) 5 m/s (C) 10 m/s (D) 12 m/s

Tardigrade Admin · Accepted Answer

Vavg = (xf - xi/tf - ti) = ((1 × 52 + 1) - ( 1 × 32 + 1)/ 5 -3) = (16/2) = 8 ms-1

Q. A particle moves in a straight line, its position (in m) as function of time is given by $x = (a t^{2} + b)$ .
What is average velocity in time interval $t = 3 s$ to $t = 5 sec$ ? (Where $a$ and $b$ are constants and $a = 1 m / s^{2}, b = 1 m$ .)

8 ,m/s

5 m/s

10 m/s

12 m/s

$V_{a vg} = \frac{x _{f} - x _{i}}{t _{f} - t _{i}}$
$= \frac{( 1 \times 5 ^{2} + 1 ) - ( 1 \times 3 ^{2} + 1 )}{5 - 3}$
$= \frac{16}{2} = 8 m s^{- 1}$

Q. A particle moves in a straight line, its position (in m) as function of time is given by x=(at2+b). What is average velocity in time interval t=3s to t=5sec? (Where a and b are constants and a=1m/s2,b=1m.)