First slide

Average Velocity

Question

A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is :

Moderate

A

4.0 m/s
B

5.0 m/s
C

5.5 m/s
D

4.8 m/s

Solution

$t_{1} = \frac{\frac{x}{2}}{3} = \frac{x}{6}, x_{1} = 4.5 t_{2}, x_{2} = 7.5 t_{2}$
Also $x_{1} + x_{2} = \frac{x}{2} = (4.5 + 7.5) t_{2}$
That is $t_{2} = \frac{x}{24}$
Total time t = $t_{1} + 2 t_{2} = \frac{x}{6} + \frac{2 x}{24} = \frac{x}{4}$
$v_{avg} = \frac{x}{t} = 4 m / s$

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